once jayne has settled on his affection for someone, whether it be romantic, platonic, familial, he's very candid in telling them how he feels. this is in part just a facet of his reckless personality and tendency to fling himself headlong into every situation half-blind with the assurance that he'll pull his own ass out of the fire like always -- but also in part due to growing up as the constant witness (and recipient and perpetrator) of purposefully with held affections. whether they were real or not.
it's also highly likely that anderson gave him one earnest 'good job' early on in his training and that completely rewired his brain chemistry. (he was suspicious and paranoid as hell waiting for the punishment, the other shoe to drop, following the praise but when it never came and he kept getting approval instead... well it fuckin' ruled.)