That's not a problem with the mod, it's a problem with your server settings.
You, or the server owner needs to put this in the INI place, otherwise you won't be able to release dinos that aren't normally on the map out of cryos.

CrossARKAllowForeignDinoDownloads=True

That needs to be in "Game User Settings.INI" otherwise you're fubar, tbch.

Thanks, I know the Ini file. :) But I found this thing really weird considering other creatures from this mod (aberrant or not) are fine.

Hmm... @KBrelax There must be a way. Haven't tamed any Aberrant Deino's on Ab yet, and my server has that setting turned off because I want to keep Aberrant Dinos only. Something's probably wrong with the server (or sp) finding that the Aberrant variant isn't native to Ab. Whatever the case, instead of using that parameter if you want to keep Ab truly Ab, try using the Dino Storage mod. There's a setting that mirrors that same setting, in a way, but only for Soul Traps and not for cryopods. Hope this helps.

The Aberrant Deinosuchus isn't the only creature it does this with. I just tamed a Aberrant Brachiosaurus and it gives the same message after cryo balled. The server setting mentioned above will work, but that will then allow flyers onto the map thus taking part of the challenge out of the map. Plus the server admin on my server will not change the setting or install a second mod to fix one mods issues. so unless there is a patch to fix the issue then my dino is stuck in a cryo ball or I have to tame another and then carry a tek generator and teleporter to transport the Brachi to different areas to gather resources. I also have not tamed a Concavenator yet to see if the bug applies to it as well.

I did not know it's enables flyers. Good thing playing single player so I don't have a problem with admins. But I'm really sorry about your problems. I know how painful is it when your dino is stuck in the cryopod. Before the TLC I mutated the deino for cave exploration. I went down, crypoded my beast....and had to make the whole journey back to my base, because of this.

the solution i found is annoying, but should work.
First enable foreign dinos using CrossARKAllowForeignDinoDownloads=True like Nerdigante said
Then in your Game.ini add the following for each of the dinos that arent't allowed in aberration: PreventDinoTameClassNames=Allo_Character_BP_C
Someone made a list that at first glance looks fairly complete here:
https://steamcommunity.com/app/346110/discussions/0/1694920442947913327/