[Babcock_Hall]

Valeur and Bradley (Chem. Soc. Rev., 2009, 38, 606–631. ) wrote, “These reagents react with carboxylic acids to form OAt/OBt active esters, which then react with amines (Scheme 5). A side-reaction can often take place with the amine reacting with the coupling reagent to form a guanidinium by-product 29 (Scheme 6),1⁴ thus order of addition and timing are crucial.” Scheme 6 shows the amine attacking the reagent.

The procedure I am following adds base (DIPEA) to a mixture of the other reagents, and a protocol from a commercial document on coupling adds HBTU to the other reagents.  Based on this information, the only order of addition of reagents I would certainly avoid is adding the carboxylic acid to the other reagents.  Thoughts?

[pgk]

I would slowly add HBTU to the acid and DIPEA mixture, in order to form the OAt/OBt active esters first. Then and after ending of the esters formation, I would slowly add the amine, in order to form the corresponding amide.

[TheUnassuming]

I've had the best luck with relatively slow addition of HBTU/HATU to the other reagents.  That said, the acid usually been my most precious material and used decent excess of amine and coupling reagent, so it could have been forming by-products with the amine and I wouldn't have noticed.
If you want to be careful, I'd go @pgk's route since the activated esters are relatively stable on their own, but as long as you don't have the amine and coupling reagent together without the acid I think you are probably safe.