I'm confused about 到 which means to arrive, or up until. How does it fit into the sentence "He was(is) caught in the act of stealing. " Also, how is past tense indicated here?
Your two questions answer each other! When 到 follows a verb, it indicates that the action has successfully completed. In linguistic terminology, it's sometimes referred to as indicating "completive aspect".
However, when you ask "how is past tense indicated here?", you should be aware that Mandarin doesn't always indicate past tense. There are a number of aspect markers (including 了、到、过), but none of these directly correspond to English past tense.
How does it fit into the sentence "He was(is) caught in the act of stealing. " Also, how is past tense indicated here?
到 here is a result complement. 抓到 can be interpreted as get caught or be caught. In this case, it's omissible.
The past tense is indicated by semantics and logics. Think about: how does the speaker know and tell it if this hasn't even happened yet? The speaker is standing here and telling it is a concrete proof that it has happened, which is an indicator of the past tense.