I had the same issue with the 880 and One. I got this answer from the Logitech forum:
"With all Harmony remotes there is a set 50ms to 100ms delay that happens between any and all commands due to it being to the way we implement the codes on the remote. Therefore it will almost never get down to a true 0ms delay as a hard-coded and built OEM remote is. This buffering (or queuing up) of commands cannot be controlled. It's just the way the hardware, firmware and software of the remote interact. In later Harmony models we were able to improve that internal delay starting from the 1100, to the 900, 700 and now 650, 600 & 300. Unfortunately, the prior line of remotes up to and including the Harmony One are more prone to noticing these "buffering" or bursting of commands"
I tried the 700 and it was better but still not like a OEM remote.
I finally switched to a URC 880 and do not notice this problem anymore. The URC, IMO, is a man's remote and makes the harmony look like a toy.