I am not having problems with this basic functionality in 2019. There has been an issue that I have see on occasion (and other users complain of it also occurring randomly), where the appearance in the program monitor is not in sync with changes made - but the changes are usually visible in the captions panel.
That is similar to what you describe, but I do not recall it happening from the beginning of editing.
First, more info: what OS, exact dot version of PR, a screenshot of your captions panel.
If you can post the srt you are importing, I can take a look.
Relatively new is the ability to change the import characteristics. Look in the Captions Panel in the lower left for "Import Settings." If you know you need to change the font style, size, etc for all your captions, this does the trick.