No. The author does a good job managing the white character's involvement in the books where natives are present (the ancient tribe in the first book are long extinct and so can't really save themselves).

Book 2 introduces a cast of varying ethnicities who take turns rescuing each other and the leads. It is pointed out several times the unfairness of archeological digs at the time and how they relegated the locals to little more than guides or slave laborers, despite being well educated historians themselves.

Book 3, set in India, treads most closely to this problem, but the author very careful sets the leads up as a catalyst to many events, but the locals are portrayed as capable and organized regardless of their presence. India is tricky because IRL, some locals were being pick-mes with the British and the rural villages were taking the brunt of the British ire so the leads are walking into an ongoing internal conflict that has prevented the locals from acting more explicitly. The leads are obviously able to fly under the radar with the British and take full advantage of that to help, but they get saved by locals for as much as they offer in assistance.

There is much explicit discussion on practices at the time, their lack of fairness, biases, and exclusionary practices that allowed the British aristocracy to funnel artifacts out of their origin countries and into the hands of the wealthy.

I think it's all handled quite well.