The Punch In / Punch Out screen is running Mas90 style (not Advanced client / server Mas200 style) over a WAN between buildings in different locations (maybe different cities). I would expect it to take 60 - 300 seconds, depending on physical distance, whether there's fiber cable, and whether there was a dedicated Internet connection instead of the normal shared Internet connection
If it was taking 5 seconds before then the Punch In icon must have been RDP connected to a Terminal Server which was really running the Punch In screen. That or Citrix connected.
There is one other thing. There's a KB article somewhere on how to setup a V/I auto-run import job to run on Advanced where it actually processes on the server instead of the normal Standard / Mas90 style (I know b/c I contributed that knowledge bit when I was there). The point is you can potentially configure the Punch In to run the same way and get back a ton of speed. Maybe your 2013 was even setup that way. You can tell by going to App Server Config and choosing Apps tab. Then check if you see a 3rd entry instead of the normal 2.