Being with both of you can only be a good thing. Particularly as during puberty he will instinctively be looking for men to instinctively use as role models as he will be feeling awkward and insecure. And if it isn't his dad it will be whoever is male and nearby.
Get him involved in a lot of activities, sports and Game,s at this age it is a good distraction for any Boy , ask his Dad to do the same . I dont think you need to worry it is good he sees his dad ,and perhaps both of you can help him taking his 'reports' to each home.
Children on autism spectrum thrive on routines. With that said, moving from one home to another may make things harder for him (most likely)
weekend visitation may work better for him
My son has PDD-NOS and he really likes his bedtime, waking up in the same room, with the same stuff, and being dropped off at school by the same parent
Good luck