Covering with grease proof paper etc helps but it will never get rid of the problem completely. Even having a separate heat press will not solve the issue as you will get migration from vest to vest.
You need to establish the perfect time and temperature for sublimating versus migration of the dye in the vest. As an example, I have two current times and temps depending on who is pressing
One is 65 seconds 172 degrees, the other is 45 seconds 175 degrees. Although the second one does migrate the dye a tiny bit.
Obviously different presses, vests and ink will have different times etc.
As a work around you can press all your hi vis stuff at the end of the day. Once you have finished, crank up the temp to 200 and wipe with a cloth to remove all the dye. You can also get a can of air spray to remove it. Once wiped thoroughly, press with an old WHITE cloth (no image) ust to check you have got everything and then turn the machine off ready for the morning