I had good intentions of looking more closely at Lusztig's papers and book but didn't follow up for some time. If it's still relevant, the following "answer" to this old question may be useful.
In the couple of years leading up to 1990 (and thereafter), Lusztig wrote numerous papers on quantum groups and then canonical basis, modifying some of his notation as needed. His book came afterward, with Part VI being devoted to braid group action. As he points out, his normalizations changed along the way, so it's important to specify which source you rely on for your formulas ("a result of Lusztig"). His 1988 Advances in Mathematics paper treated only the ADE types in $\S5$, superseded in his 1989 Geometriae Dedicata paper by a more general and somewhat different set-up for braid group action in $\S3$. Part VI of his book adopts a more comprehensive viewpoint, incorporating in the operator notation a sign $\pm 1$. (See the notes and references at the end of Part VI.)
Your notation seems closest to what is used in the 1989 paper, but you've omitted the generators $K_i$ and $K_i^{-1}$ which play an essential role in the formulas for the action of $T_i$ on $E_i$ and $F_i$. So I can't yet reconcile what you've written with that paper of Lusztig. In any case, you need to be more precise about your references, since he wrote so many relevant papers including those on the canonical basis.