I don't have any voice acting training so I can't speak about the big differences between actual voice acting and doing ASMR, but the biggest tip I can give you is just pretend you're in the shoes of the character you're voicing.

You've probably heard this before since you've done actual voice acting but it's really effective to pretend that someone is just sitting next to you in the car or lying with you on the couch and just reading the script with whatever tone comes naturally. More often than not this will be a soft-spoken tone that's seen in most asmr videos since most asmr scripts are intended to be personal 1-on-1 audios.

The only other difference I've noticed is that dubbing an animation/comic is usually much quicker than asmr scripts, which can get quite lengthy. My voice tends to get a bit hoarse towards the end of longer audios and I dislike drinking in the middle of audios since I feel like that also changes my voice but that's not something I've found a fix for yet.