Hi Niwantha,
Using an analogous example below:
This is a boring lecture.
The students were bored.
Both "boring" and "bored" are known as participial adjectives. The difference between them is that something that is "boring" causes someone to be "bored".
"Boring" is a characteristic of the lecture. Feeling "bored" is an end result of something "boring".
Thus, for your question, "mature" and "matured" are adjectives.
He is mature for his age. ("mature" is an adjective describing his personality.)
He has matured over the years due to his experience. (Something causes him to become "mature"; therefore, he has "matured".)
With these points of consideration, your sentence 1 is correct. Sentence 2 sounds odd as it does not convey it's intended message.
Correction for sentence 2: He has matured.
Hope this helps.
Cheers,
Lance