Priming sugar

I bottled my first beers today but a little worried on how I primed it, I used 4.5 oz for 5 gal nut brown ale, I'm not worried about that part, part I'm worried about is that I boiled 2/3 cups of water only and then added sugar to it, shut heat off and let stand for 10 min, I then for some reason began to syphon beer into bottling bucket without the priming sugar, I got maybe a couple of inches of beer before I realized, shut syphon off and then added priming sugar, is this something I need to worry about? Im thinking it might not of mixed evenly? It's bottled though, just don't want to flat of beers or bottle bombs, any advice would be great. Thanks

Your beer should be fine.

Perfect. That's the way I do it. Adding boiling, or near boiling, water to a plastic bucket seems to leach some plastic flavors. HDPE is rated to 190°F. although the bucket will survive higher temperatures it's probably best not to exceed that.