I think "allonger sur le temps de réaction" means nothing. It may be "allonger le temps de réaction" ou "le temps de réaction s'allonge". And indeed, it means "augmenter", "étirer". I personaly would use "rallonger", because rallonger means "augmenter la longueur" lenghten and only that.

Allonger in this sentence means lengthen.