"After adding the hops I appear to have activity in the air lock again and even the beer appears to have activity in it (I can see the hop particles swirling) like it's fermenting again."
By chance, did you check wort pH before fermentation and at the time when you assumed fermentation ended and again when the beer was dry hopped? It isn't a bad practice. Then, if something unusual occurs especially, if it involves fermentation you'll have a baseline to work from. A type of bacteria strikes during second fermentation, Gram-Neg type. It kicks up the beer. It might be coincidental that bacteria struck when the hops were added. If a pH test was utilized a determination could be made. If pH continued to reduce to a level that wipes out yeast and the beer is working, Gram-N bacterium is the culprit. Besides, yeast needs O2 for it to work and beer is void of O2 when it's that far down the line, until hops are added. Then, the O2 in the hops causes the beer to stale. When beer is sugar primed, yeast strips the oxygen molecule from sugar and uses it as the oxidizer and that's OK.
Since, the beer was dry hopped after one week in the secondary fermentation vessel, how are you sure that fermentation had ended before hops were added? Do not assume that a stable hydrometer can determine when fermentation ends. The test was performed during a single snap shot in time.
If by some wild chance that some maltose was released by Beta during the brewing process and since the beer was left on the yeast for three weeks before transferring to second fermentation vessel. This is what occurred; yeast during primary fermentation burns up all of the simple sugar, Glucose, and the majority of alcohol is produced during that time. After Glucose was wiped out yeast began to work on complex sugar. The beer being already in second fermentation for a week was transferred to secondary for one week before it was dry hopped. During second fermentation yeast absorbs maltose through cell walls and enzymes within yeast convert maltose, a complex sugar back into glucose, a simple sugar and fermentation continues because Glucose is yeast fuel. All of that stuff should have ended when the hops were added. If yeast restarted, something is out of balance. But, it might be OK, this time.
"don't worry about it its just oxygen releasing from the hops"
Yes, and it causes staling of the final product. That's why Randall's are manufactured. Besides, the pH level of beer is too low to extract hop aroma that sticks to the final product.
It's not a bad idea to look at the Beta number on the hop bag. It's there for a reason. The closer the Beta-Alpha number, the finer the hop. It is balanced.
"Hops have some sugar in them"
100% correct. There is a special type of sugar in hop flowers but, it doesn't affect fermentation. There is nothing in beer that is capable of extracting the sugar. If the sugar could be extracted during dry hops I am not sure if the sugar would be complex or simple type. It would be a factor to consider when dealing with fermentation. Yeast can only use simple types of sugar for fuel. Basically, don't get spool up over fermentation during dry hopping, unless it occurs. If it occurs, it shouldn't have.