The versions of games on the SNES Mini usually have their VC patch applied,and that's normally the cause of the epilepsy protection. On the NES Mini, there was a global settings that looks for certain flashing and fixed it on the fly. With the SNES, the protection is done through patches.
Of the 21 games on the SNES Mini, 14 of them have VC patches. Really the best way is to consider these new versions, like F-Zero only had a 1.0 release but the one on the SNES Mini is effectively
(but not literally) 1.1. But yes, these versions do include the epilepsy protection. For example, let's look at the Link to the Past patch, which MathOnNapkins previously broke down. You can see, this is an anti-epilepsy patch.
0003A50D: 03 18
0003A50E: 03 18
Adjusts two consecutive entries in a data table. Those extend the last two states in the Ether Medallion animation to make them last 8 times longer.
00067E6F: 1F 05
Modifies the immediate operand of a LDA instruction. This lowers the intensity of the flashing colors that tint the title screen as the sword is dropping into place. Instead of cycling between tints of full intensity red, green, and blue, it's now cycling between dull red, green and blue.
00075805: 0E 02
00075818: C0 40
00075819: 01 00
0007582C: 38 08
Modifies immediate operands to ADC instructions in a routine that adjusts colors to gradually tint more towards white. IIRC this is used when the seal on Ganon's Tower is being broken by the Crystal Maidens. The tweaks put in place cause the flashing process to take about 7 times longer.
000DE03C: 72 70
000DE03E: 9C 95
000DE040: FF 57
These modify the lower bytes of entries in a large table full of palettes. The first two reduce the red component, and the last change reduces the red and green components of a color. Which palettes? It would take more effort I'd rather not do at the moment to figure that out. Best I can say at the moment is that they are palettes meant for BG tiles in indoor parts of the game. Specifically, my notes mark them as "DungeonMain BG palettes (6 in each group)"
If you want to look at the 14 VC patches uses on the SNES Mini, I've uploaded a zip here: http://robin64.co.uk/files/snesVCpatches.zip
BUT! On top of that, there are also a few in-memory patches which get applied on top of the already applied VC patch when the game boots. These aren't dumped with the ROM, so they had to be extracted at runtime, thanks to rhester72 for doing that. Most of these are tiny and nobody has really looked into what they do. There are 12 of these, and not all games with a VC patch have one. A task for someone clever, one day, would be to look into what these do! You can grab there here: http://robin64.co.uk/files/snesmempatches.zip