No, not unless you want something to happen at those exact times. Your existing rule will run the actions whenever there is motion, which is probably all you want--just wanted to make sure since you did say that time was "trigger" (assuming you just meant "condition"). You can have multiple triggers (or none if you know what your other options are), but again, I don't think you need to here.
I strongly recommend reading the Rule 4.0 docs before diving in. (I can see nobody has clicked that link yet. 
The videos are fine but won't teach you everything you need, unfortunately.) As I mentioned, there are a few problems with your rule as a substitute for Motion Lighting. The motion lighting example the docs avoids this problem and will get you pretty close to what you want, but you'll have to add in your time conditions somehow. How/where you add it will depend on whether you want to restrict both the "on" and "off" actions or just the "on" action, among other things. There are also multiple other considerations you can make and several ways you could use or modify the examples (of which the above is only one) to suit your exact need.
That being said, I'd probably stick to Motion Lighting for this: it's a smaller app and will likely run faster (probably not much but a few hundred milliseconds, maybe--still, any amount of speed is great for indoor lighting automations, I think). Even for your example, Simple Lighting (soon to be renamed Simple Automation Rules) could handle things if you want to restrict both "off" and "on" actions in one rule (or make two, one for each, with whatever restrictions you do or don't want). But none will work if your sunrise and sunset times don't seem to be working correctly, which others' advice above may help you figure out. And there's certainly nothing wrong with learning RM, just wanted to point out that there are easier ways to do this.
Just to be clear about the problem: what "continues" beyond sunrise+15? The only thing that you should see happen if it's later than sunrise+15 (but before sunset-30) is that the "T" you currently see next to "Time between sunset-30 and sunrise+15 minutes" will change to an "F" (assuming you either reload the page or didn't already have it open--again, it doesn't dynamically update). Your screenshot above is definitely correct in this regard given the current time in your time zone, but I know you said this is the time you weren't having problems with, so I guess that's not terribly revealing.
