Autism is characterized by language delays, delays in social development, and the presence of repetitive behavior (e.g., rocking, need to have things the same). I am glad that your son is in a school that you like and that he is receiving speech services. If you or his teachers are noticing repetitive behavior or social difficulties, I recommend that you have your son reevaluated by a professional with experience diagnosing autism spectrum disorders.
It would be useful to work with a professional who could help develop a behavior plan to decrease your son's tantrums. The website of the behavior analysis certification board (www.bacb.com) has a list of certified professionals by state. Like any other developmental or behavioral issues, it will be important to address this problem as early as you can so the your son can meet his full potential.
The general strategy is to teach your son that tantrums are not the way to "get his way." Effective interventions generally consist of two components. First, it is important that tantrums do not result in any improvement. For example, you mention that teachers provide affection after a tantrum. If he enjoys this affection, this practice may actually increase tantrums. I recommend that you work with a qualified professional and your son's school to identify a consistent way to respond to his tantrums that is unlikely to reward tantrums. For example, it can be effective to remove young children briefly from ongoing activities (e.g., have him sit in a quiet area of the classroom). Minimize attention to the tantrum while protecting the child and his peers. When he is calm, simply return him to the ongoing activity.
This strategy will be effective only if your son has more appropriate ways to communicate what he wants. Speech therapy will help with this. Also, adults should try to honor his appropriate requests for attention and preferred activities as much as possible (and within reason). Also, provide attention or other rewards when he is engaging in other appropriate behavior such as playing with peers. If he enjoys cuddling, adults should make time for this when he is behaving appropriately and avoid cuddling him after tantrums.
These are the general strategies. A behavior analyst will be able to help to you adapt these strategies to your son's individual needs and preferences. It sounds like your son is a warm likeable child who will do well with some additional support.