Negative predicted values after xtnbreg on nested count data

I am analyzing how many comments a social media picture of a women gets based on how good looking the woman in the picture is and the extent to which her image has been altered (e.g., heavy make up, photoshop, cosmetic surgery). The dependent variable ( photo_comments) is count data and the predictor variables are continuous and have been standardized to convert them into a common scale ( z_altered and z_fem_beauty). Because the data are nested within the poster's account and overdispersed, I use xtnbreg to conduct the analysis and used xtpoisson as a sanity check.I use the number of followers to the account as the exposure variable.

Code:

. sum photo_comments, detail

                       photo_comments
-------------------------------------------------------------
      Percentiles      Smallest
 1%            0              0
 5%            0              0
10%            0              0       Obs               5,866
25%            0              0       Sum of Wgt.       5,866

50%         18.5                      Mean           5435.123
                        Largest       Std. Dev.       27906.4
75%         1055         430655
90%         8770         481069       Variance       7.79e+08
95%        25388         803284       Skewness       19.18279
99%       122844        1139151       Kurtosis       616.2378

When I run the margins command after xtnbreg, I get negative expected values for the count, which doesn't make sense. Do you have any explanations for why the predicted values are negative?

Code:

 xtnbreg photo_comments  c.z_altered##c.z_fem_beauty,  exp(followers1) fe

Conditional FE negative binomial regression     Number of obs     =        481
Group variable: account_id                      Number of groups  =         65

                                                Obs per group:
                                                              min =          2
                                                              avg =        7.4
                                                              max =         34

                                                Wald chi2(3)      =     167.11
Log likelihood  = -3886.7958                    Prob > chi2       =     0.0000

--------------------------------------------------------------------------------------------
            photo_comments |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                 z_altered |  -.7177536   .0586089   -12.25   0.000    -.8326249   -.6028823
              z_fem_beauty |   .2723421   .0607985     4.48   0.000     .1531793    .3915048
                           |
c.z_altered#c.z_fem_beauty |   .3414562    .052084     6.56   0.000     .2393735     .443539
                           |
                     _cons |  -17.93335   .0660347  -271.57   0.000    -18.06277   -17.80392
            ln(followers1) |          1  (exposure)
--------------------------------------------------------------------------------------------

margins ,at(z_fem_beauty= (0 1) z_altered=(0 1))


------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |  -4.021224   .0660347   -60.90   0.000     -4.15065   -3.891798
          2  |  -3.748882   .0918066   -40.83   0.000     -3.92882   -3.568944
          3  |  -4.738978    .093584   -50.64   0.000    -4.922399   -4.555556
          4  |  -4.125179   .0923395   -44.67   0.000    -4.306161   -3.944197
------------------------------------------------------------------------------

When I conduct the same analysis and margins command using xtpoisson, all the predicted values are positive, as they should be.

Code:

. xtpoisson photo_comments  c.z_altered##c.z_fem_beauty,  exp(followers1)  fe

Conditional fixed-effects Poisson regression    Number of obs     =        481
Group variable: account_id                      Number of groups  =         65

                                                Obs per group:
                                                              min =          2
                                                              avg =        7.4
                                                              max =         34

                                                Wald chi2(3)      =   72928.93
Log likelihood  = -1280726.3                    Prob > chi2       =     0.0000

--------------------------------------------------------------------------------------------
            photo_comments |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
                 z_altered |  -.1015437   .0009827  -103.33   0.000    -.1034697   -.0996177
              z_fem_beauty |   .0826125    .001004    82.29   0.000     .0806448    .0845803
                           |
c.z_altered#c.z_fem_beauty |    .119922   .0006979   171.84   0.000     .1185542    .1212898
            ln(followers1) |          1  (exposure)
--------------------------------------------------------------------------------------------



. margins ,at(z_fem_beauty= (0 1) z_altered=(0 1))


------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   13.91212          .        .       .            .           .
          2  |   13.99474    .001004  1.4e+04   0.000     13.99277     13.9967
          3  |   13.81058   .0009827  1.4e+04   0.000     13.80865    13.81251
          4  |   14.01311   .0010905  1.3e+04   0.000     14.01098    14.01525
------------------------------------------------------------------------------