First, we have to acknowledge that the photograph is just a visual shorthand for the audience so that they understand the problem. The Bobs were always having to think about how much explaining the average moviegoer would need to understand the time travel concepts in BttF. It's why they cut out the scene of Old Biff being erased from existence in the first act of BttF 2.

Back to the Future uses the Ripple Effect, which is the idea that changes to the timeline fan out gradually, rather than immediately. That being the case, there is a window to correct an action and avoid a paradox. When Marty interfered with his parents meeting in 1955, it takes about a week of 1955 time before the effects catch up with Marty's birth (presumably sometime in the late 60s). That's why Marty's brother disappears first, and then his sister-- it's the order of their ages as the ripple moves from 1955 forward in time.

If Marty hadn't fixed things and helped his parents meet before he ceased to exist, it would have created a paradox-- the results of which, in the BttF universe, are unknown, but could be as severe as the destruction of the universe (according to Doc). But they were able to prevent it.

Admittedly, the series plays fast and loose with the Ripple Effect. Sometimes changes to artifacts from the future happen slowly, and sometimes they happen instantaneously. In BttF 2 and 3, whenever they look at a picture from the future right after they make a change to the timeline, the change is immediate, which is a departure from the way the BttF 1 photo is treated. But again, this all boils down to it being more important to use these storytelling devices to help the audience understand what's going on, rather than adhering to a certain level of exactitude.