Nothing implies causal determinism. It is just a theoretical idea.
Principle of sufficient reason has nothing to do with determinism. While determinism assumes that prior events only are both sufficient and necessary reasons for everything, the principle does not make that assumption.
Determinism assumes that prior events sufficiently determine their effects with absolute accuracy. In reality, there is probabilistic inaccuracy in all events. The effect is only partially determined by the cause.
Determinism assumes that prior events are the necessary reason for everything. The principle does not require past events. The reason can also be a purpose in the future. Voluntary actions are done for a purpose instead of due to a cause.