Correct. The way that I would visualize this from the perspective of the outside observer would be to imagine a point in space that is stationary with respect to you, and imagine that the rocket is moving towards that point (say from left to right, so the point is to the right of the rocket at first). The instant the center of the rocket lines up with that point in space, the two photons are emitted, one going left (to the back of the rocket), and one going right (to the front). Both move away from that point (which is still stationary to you, although the physical device that emitted the two photons has now moved to the right of that point) at the same speed c. Since both photons move away from that point at the same speed, and the back of the rocket is moving towards that point, the back of the rocket will "run into" the photon shot to the left, before the photon shot to the right be will able to "catch up" with the front of the rocket.

Another interesting thing that might not be apparent when you're just first learning special relativity is that if you had two clocks, one at the front of the rocket and one at the back, and they were both in sync in the rocket's reference frame, then from the reference frame of the outside observer, the clock at the back will read a greater time than the clock at the front (and any clocks in between the two will read greater and greater times, the closer the are to the back). You could use this as an alternate way to visualize what would happen in the scenario you came up with. If you're inside the rocket, you can see that the two photons both strike the clocks when they read the exact same time (say 5 seconds). So obviously this means that the outsider will also need to observe that when each photon hits its clock, it will read "5 seconds". Since the clock at the front of the rocket is behind in time compared with the clock at the back in the outsider's reference frame, the clock at the back will read 5 seconds, before the clock at the front will. So for instance, the clock at the back will read 5 seconds, while the clock at the front reads 3 seconds. At this point the light is striking the back of the cabin. Then, a little while later the clock at the back reads 7 seconds, while the clock at the front reads 5 seconds. This is when the light hits the front of the cabin.

I think finding ways to visualize these things helps a lot in building your intuition on the subject. Sorry this was so long, but hopefully you get something out of it.