In most cases the letter will find its way to your friend regardless of whether it went to the main site or the annex. Correctional facilities that operate multiple sites on the same campus or within the same system typically have mail forwarding procedures in place for exactly this situation. Staff at the receiving mailroom generally know where to redirect mail when an inmate is housed at an adjacent or connected site.
TCIX, the Turney Center Industrial Complex in Only, Tennessee, operates both a main facility and an annex, and correspondence between the two sites is handled internally without requiring you to resend or take any additional action in most cases.
If for any reason the letter does get returned rather than forwarded, it comes back to InmateAid's Florida address rather than to you. When that happens InmateAid investigates the reason, corrects the facility information, and resends the letter at no additional charge. That backstop means a misdirected letter does not simply disappear or require you to pay again to fix the problem.
To avoid the uncertainty going forward, the quickest way to confirm which site your friend is housed at is to call TCIX directly and ask. Tennessee Department of Correction also has an offender search on their website where you can look up your friend by name and confirm the exact housing assignment. Once you have that confirmed, updating the profile in your InmateAid account ensures future letters route correctly from the start.