Kenneth Fisher discusses how to get MSDTC working with Integration Services:
tl;dr; The MSDTC service has to be not only turned on, but configured on all of the machines involved. Including the machine running the SSIS package (possibly a workstation).
Configuring remote MSDTC, sure. Configuring local MSDTC, though, is something I hadn’t realized was important, at least if you want to use SSIS transactions. Probably goes to show how often I use SSIS transactions…