Yeah I wasn't having any issues on the Xbox after dedicated servers went down either, seems the Switch has it's own version of the glitch that still needs fixing.
Here's some info I found on it:
"Has nothing to do with players joining. In fact it is more likely to occur in a full lobby than not. Your wrong counselor loads with their default costume, but you retain the perks of the counselor you actually selected. Usually causes a mish mesh Jason if you're selected, and tends to ignore counselor/Jason spawn preferences. Also causes you to skip the match intro."
"On Switch, this is due to how quickly the system accesses the save and game info, if I'm not mistaken. That's an interesting turn for some of the things you've seen improve, like intros."
As I mentioned there is a fix you can do but only for the digital version of the game: https://www.reddit.com/r/F13thegame/comments/kov8lr/possible_fix_for_random_counselorjason_on_switch/?utm_source=amp&utm_medium=&utm_content=post_body
I tested a theory last night that seemed to help a little bit: making sure you have a Jason selected seems to help you get your preferred counselor. My girlfriend had her Jason set to random (she hates playing as him) but after I had her select one she ended up getting her favorite character, Tiffany, a lot more. 6/8 games we got our preferred characters whereas before she got Tiffany a lot less than I got Adam.