I have one toilet that did a similar thing. It probably isn't anything to worry about. It sounded to me that the valve didn't open fully at first, then after it was running for a few moments, it opened up. After a few months, it stopped doing that 2-stage thing. If it bothers you, you could change the fill valve. First, though, make sure you don't have a problem with the shut-off valve - make sure it is fully opened and then see if you can recreate the problem by turning the valve part way closed (you wouldn't want to leave it that way, but try it as an experiment).