Is this SimpleActionClient instantiation thread-safe for the callbacks?

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First, I am constructing an instance of the template class SimpleActionClient as follows:

actionlib::SimpleActionClient<MyAction> client(nh_, "topic", true /*spin_thread*/);

Later I am assigning callbacks (done_cb, active_cb, feedback_cb) with sendGoal.

Will those callbacks be thread-safe since they use the same global spinner or would they not be thread-safe in this case since the spinning is done in a separate thread?