This is an issue only certain servers seem to have, and my testing server isn't one of them.
You could try the following very simple Lua edit:
Open the script /garrysmod/gamemodes/terrortown/gamemode/init.lua
Make a backup copy, the change might cause other problems.
Find this around line 387:
-- Finally, get players in there
--timer.Simple(0.01, SpawnWillingPlayers)
SpawnWillingPlayers()
Change it to say:
-- Finally, get players in there
timer.Simple(0.01, SpawnWillingPlayers)
--SpawnWillingPlayers()
So you basically remove the "--" and put them on the next line there.
Save/upload and switch maps on the server.