I live in Grand Cayman and I'm going back to the Philippines for vacation. To get a cheaper fare, I applied for a transit visa to Canada and was approved. My question is, am I allowed to go out of Vancouver to visit my brother who lives there?
Except for people transiting directly to U.S. preclearance, everyone who transits Canada will pass through immigration control and end up landside. Much like in the U.S., and with the exception noted, Canada does not have sterile international transit areas.
On your itinerary, you will pass through immigration and be in the arrivals hall. You are allowed to leave the airport. Indeed, the transit visa is one of Canada's temporary resident visas, albeit one that only allows a 48 hour entry.
Whether you can visit your brother, then, depends on how much time you have between your flights.