This post suggests that p-value follows uniform distribution in case of point null hypothesis and continuous data.

In my project, I have millions of p-values from actual data. I don't want to get into the details of my data and statistic test. I just want to know the following:

In general, for point null hypothesis and continuous data, if the p-values do not follow uniform distribution, does it imply that 1) the null hypothesis is not correct, and/or 2)that applied statistic test is not appropriate? could there be other reasons?

Thanks,