A good PM is always doing both strategy and tactics - always. I like to joke that we have two eyes and PM's need to fix one on the present and the other on the future. Put another way, if you want to build a path across a bog you need to place each step (each release) squarely in line with where you want to go.
Perhaps the best comparison is with a rock climber tackling Yosemite's Half-Dome. Climbing is a complete fusion of strategy and tactics - the two are inseparable. You have to research the best route options but, having selected one, you have to study the terrain intimately down to the nubs and crevices to be able to execute the climb. Conversely, if you can execute 11c climbs that affects your route strategy.
A product manager can pick any old market segment and claim "Gartner says the business is here," but good product managers dig deep into the reality of the customer needs to produce a product roadmap that delivers revenue-worthy product value in that segment that is deliverable by his or her engineering team. To correctly steer a roadmap, you have to learn the nubs and crevices of the customer terrain and know your dev team's core competencies. Great products are carved from the muck of customer reality and intimate self-knowledge.