Yes, the system band plan applies to every site in the 157 system.
It's important to note that the system itself doesn't use the band plan per se, it's the radios that use it to determine the channel frequencies at each site. The band plan exists in two places: It is continuously broadcast over the control channel, and it is programmed into each radio.
Motorola numbers the band plan entries from 1-16, while other radios, scanners, and software generally use 0-15 or 0-F (F is 15 when converting HEX to DEC). The order of the band plan entries are critical, as the channel numbers correspond to each position in the table.
In the case of your Uniden scanner, you should almost never need to manually program the band plan. The scanner should receive it from the control channel and automatically fill the table in without user intervention. I'm very surprised that it got wiped out in your 536 and didn't repopulate itself automatically after a few seconds of monitoring the control channel.
I would suggest clearing out all of the band plan entries in the 536, power cycling the scanner to write the changes to the microSD card, then turn the scanner back on. Scan the Tinker site for a minute or two, then check to see if the band plan has repopulated itself in the programming. If it has, you're good to go...if not, something else is going on like perhaps the control channel has stopped broadcasting it, which is highly unusual but I suppose possible. You may want to try the same with the 436 to see if the results are the same.
Oh and obviously make sure both scanners are at the same firmware, the last release was 1.25.00 which is technically a beta release but has been out for half a year.