I would assume that once a golfer reaches a certain age he automatically qualifies for the Senior's Tour. Yet I've seen Tom Watson participate in both. By doing that he's taking the place of someone who more likely needs the experience of the PGA Tour, more so than him. Why is this allowed?
Same reason people can play in PGA and European Tour events, its just a different tour. In order to stay on the PGA you need to earn a minimum number of points in a season, so some seniors will pick and chose their full PGA events in order to maximize their chances of earning the points they require to stay on the tour, and play in the senior events the rest of the year. For example, there wouldn't be much point in a senior entering a PGA event at Oakmont, with its 300yd par 3, however at a shorter course they would feel they would have a good chance of making the cut.
In the case of Majors like The Masters, and The Open, previous winners are invited back every year, regardless of PGA membership
There is nothing altruistic about any of the professional golf tours. Success - either winning tournaments, money earned, or world rankings - qualifies players for entry into tournaments. Other players gain entry either by sponsor's exemptions or by qualifying in Monday qualifying rounds. This is probably how someone like Tom Watson gains entry into a regular PGA Tour event. The Senior tours limit entry only by age. Players must still qualify by the criteria set up by each tour. The PGA Tour has no age limits for entry. Simply put, if you are good enough, you get to play. Players with past success like Tom Watson are granted entry either by sponsor's exemptions or by some other qualifying means. For example, US Open winners are granted a 10 year exemption into tournaments on the PGA Tours. If a younger player wants in, he has to play his way in. It's as simple as that. It's the ultimate survival of the "fittest". In this case fitness is judged by how well you play tournament golf.
Other tournaments, like the Masters, grant entry based on several different criteria. They make places for amateurs, players with success on other tours besides the USA PGA Tour, and all past winners are granted entry. Regardless of the criteria, however, all these players have played their way in. When Tom Watson was young, no one granted him entry into any tournament because he needed the experience. He had to earn it first.