Lyman, neither you nor I can even begin to assume what the pilots were thinking or trying to do. In this case you have provided a phrase which out of context appears to be ambiguous as to the sequence of events. I have suggested that elsewhere in the report it is fairly clear as to what they mean (I'm not going to dig it out now - jetlagged to buggery).
The acid test is to look at the DFDR trace - the nearest to raw data we have, and see what was going on with the data. By telling me that I can't do that not only have you shut off the most effective avenue for resolving the ambiguity, but you've made it look like you have some reason for not wishing to do so.
So, for your benefit I'll use the fact that in the "1.1. History Of Flight" section, the BEA have placed events which happened either concurrently or in very quick succession into small, concise paragraphs, each of which starts with a timecode. The extract you provided is contained within one of these paragraphs. I put it to you that if there was significant lag between the aircraft pitching towards +10deg and the aircraft only starting to climb once +10degrees was reached, then this would have necessitated separate paragraphs for each event.
For the rest of us, let's look at the trace. The aircraft reaches +10deg nose up at approx. 02:10:16. At this point vertical speed is already approx. +3000fpm.
The climb begins in earnest (i.e more than +1500fpm) with the pitch attitude between 4 and 5 degrees.
As an aside, in my business it is vital to understand when events are happening sequentially versus concurrently, because the consequences to design philosophy and problem-solving are very different depending on which method is used. In the best-case scenario, the documentation is very explicit as to this, but I've read my fair share of lousy documentation from which it has to be inferred. Not to blow my own trumpet, but I'm pretty good at distinguishing these inferences based on context these days...