Time and duration were two important concepts in Bergson's philosophy.
Einstein's two theories of relativity (special relativity and general relativity) led to a new concept, spacetime. So both the philosopher and the physicist are referring to the concept of time in this context. For Berson, time should not be "limited" to what we can measure by means of a clock; this was not a meaningful definition of time. As the article explains, Einstein disagreed:
He mentioned two common ways of thinking about time, psychological and physical. Psychological time was the time perceived by a person, while physical time was time as measured by a scientific instrument, such as a clock. Time as measured by an instrument was often different from time perceived by a person. (...) “The time of the philosopher, I believe, is a psychological and physical time at the same time,” he explained in Paris. But relativity, by focusing on very fast phenomena, had shown just how off-the-mark psychological perceptions of time really were. Psychological conceptions of time, Einstein insisted, were not only simply in error, they just did not correspond to anything concrete.
So "Il n'y a donc pas un temps des philosophes" means that there is no separate philosophical concept of time or, more literally, there is therefore no philosophers' [concept of] time.