When a child is at school... and doing so many things, it is "work" and tiring for a child to be on point and behaved and on it, ALL day.
When they come home, they need to deflate. Deflating often means that they are getting out all of their "yah-yah's" and what not. It is not easy for a child, to be in school all day listening to direction and sitting still and etc.
They get pent up and just plain tired, and or are hungry when they come home.
Much like an adult that comes home from a LONG hard day at work and acting a certain way, doing things for others, following direction, and trying to be perfect about it all.
My daughter, was/is like that too. I know her cues, and I KNOW she is just deflating from a long hard day at school. I am thankful that my girl is so well behaved at school and is the perfect student...but when she comes home, all her pent up whatever, comes out. I don't censor her to the point that she can't unwind, but I know there will be a moment where she is just deflating and needs to.
A child, to a certain extent, has to have a place where they can vent/unwind/deflate, too. Otherwise, we cannot expect them to just "behave" like a robot all darn day. Kids have their threshold too, of what they can or cannot manage. Us, as adults, need to "vent" too at times, and we do. But for kids, adults are always expecting them to behave ALL day. What a doozy for a child. And, at 3 years old... it is a hard age anyway. So MANY expectations upon them... sometimes their tiny shoulders just cannot carry it all or the burden.
Tell your son, he can unwind... but not to "hurt" anyone. To try his "best"... not being perfect... that you know he IS a good boy.
While he is tantrumming... don't "stop" it per say... but tell him go in his room... let it out. That is his safe place. Then when he deflates (and a child will deflate after letting it out), then go to him, talk with him calmly, tell him you love him and you know sometimes it is just hard. But you are a TEAM... and that is what Mommy is for... but he can "help" you too.
Kids often, even if irked, need validation... because they cannot always cope with their emotions either and need help. And if they know you are not going to punish them for it... for an honest feeling, but HELP them cope... even if it is punching a pillow TOGETHER... then they will often just key down themselves. Teach him alternate ways of getting out his yah-yah's.
Just some quick thoughts.
All the best,
Susan