Unfortunately, I I'm not familiar with how to check logs or use the debugging console, but I think I should mention it.

On Afterbirth+, no Repentagon.
First successful run with Tainted Isaac was OP, so I did Mega Satan for fun.
No achievement or unlocks, as expected with the mod running.
The real goal was spindown from killing Delirium, anyway.

After killing Delirium and touching the chest to complete the run, I was briefly teleported into the Mega Satan room with pop-up message of "Fixing Mega Satan Unlock", or something to that tune.
Then it immediately cut to the ending cinematic and I got both the Delirium and Mega Satan unlocks/achievements.

I'm not sure if that was an update to this mod or one of my other ones. I can post my modlist if you'd like, but I am mostly just confused because I remembered that this mod's Description page states that it breaks the unlocks/completion (rather than still getting them with whatever that little workaround was).