If ever I passed through immigration in Incheon (with Filipino citizenship, US tourist visa and LA as my final destination) and my choice of free transit tour is not available or full already, can I commute there on my own instead?
You can only pass through immigration and thus exit the airport if you can get a visum. Since the Philippines is not on this list: https://en.wikipedia.org/wiki/Visa_policy_of_South_Korea You need to apply for a visum in advance.
Some airports have these "free city tours" for these tours you do not clear immigration and thus does not require a visum.
The fact that you hold a visum for the US does not make a difference for South Korea.