The interesting thing is that the actual variable doesn't appear to be being changed, as we see in the video at 0:17 that the host_timescale is still set to the default of 1.0 (normal speed). Either host_timescale is being changed invisibly, or the problem lies elsewhere...
Some questions/tips that may or may not help:
-Are you rebooting TF2 after each compile, or using -hijack?
-Does the problem persist in official maps, or only in your map?
-Have you tried booting up TF2 without running a Hammer compile, and then opening an official map? If this does fix the problem, does running your map cause the problem to reappear?
-Did you try checking your game files?
-Any strange compile or console errors?
I'll try these out and let you know the results.
I reboot TF2 after each compile, and I'm not using -hijack.
The problem is persistent to only my maps, even if I load up the map straight from the console.
I've tried running an official map first before running my map and the problem appeared only when I ran my map.
I verified my game files and the problem is still there.
I used interlopers.net to check my compile log and it appears that there are no compile errors.
In console, there doesn't seem to be any errors, but it does say that there is no map config, no listenserver config, and the tf_server_identity_account_id was not set.