I'm not a big fan of weed-n-feeds. They neither weed nor feed well. You're better off in the future getting them in separate products. For now, share the info
@Jeffersonzoysia asked above and we can give you an idea of when you will need to reapply each. Most of us apply pre-emergent in two 6-month applications (spring and fall) or four 3-month application (called a split app). Some of us will use two different pre-emergents to have multiple modes of action and offset them. I use Simazine and Prodiamine. It doesn't have to be that complicated though; the Dimension you applied has an active ingredient of Dithiopyr which is very similar to Prodiamine. That will help a bunch keeping the weeds at bay. We just need to figure out when you need to reapply.
For fertilizer, most of us will apply lower rates but more often (called spoonfeeding). This keeps the N more consistent and prevents growth surges where you are having to mow like crazy. For reference purposes I apply .125lbs of N/1000sf each time I spray PGR on my Empire Zoysia. That is about twice a month right now but will be up to three times per month in the hot months. Again, it doesn't have to be that complicated. You can put it down each month and as long as you are not pushing high amounts per month you won't see much of a surge. I hope I'm not making it more confusing. It's just better to track your pre-emergent seperately from your fertilizer. The timing does not normally match... at least for me it doesn't.