does every program needs to be turing complete?

Not really, since programmable machines predate real-world turing-complete computers by at least a century.

https://en.wikipedia.org/wiki/Jacquard_machine

Only if you define programs as instructions for manipulating Turing machines.

To be pedantic, we can define a non-Turing-complete subset of a Turing machine's instruction set, and pass combinations of these instructions to the machine, and that could still be called a program.