For someone with an ASD, we tend to get through our days, then process everything later when its quite and we can think.
But this is arguably the same with life. Going through the teenage years is a rush, we are discovering everything, trying to be the best at stuff, and trying to make everyone like us. When all this dies away as we go into our 20's, we are able to think and start processing everything. Reliving old memories and working it all out, etc.
But don't dismiss all the things you know, the experiences you've been through, etc. You aren't emotionally immature, you're living a different life. Our environments and experiences shape us. If you view someone else as emotionally mature, maybe it's just because they've been through different experiences that have shaped them differently.
If you've been through the same experience and it didn't affect you as much, maybe you were just dealing with something else at the time, or had a thicker skin, or it just affected you differently.
Either way, your most likely as strong and mature as them, but in a different way. You've adapted to your circumstances, and can probably deal with things that they cant, and vice versa.