I think the problem you have is the fact that Astarion, even if played as the player character, will always run off to the shadows (if you didn't ascend, and it sounds like you didn't) before Karlach explodes. So there is no chance for Astarion to say his final goodbyes or to convince her to go to Avernus. What is at fault in this scenario is the timing, it always happens like that, in both versions. If played as Astarion and if played as anyone else.
But you should see this cutscene as his proper ending:
Which I am betting you didn't get to see either (it's either this or going to Avernus with Karlach) because patch 4 messed up a lot of ending epilogue sequences.
The only way for Larian to fix this shit is to rearrange the dock cutscene sequences, so Astarion doesn't fucking burn at all (it is sunset/evening after all) or he runs off AFTER the big Karlach choice.
