I made a diagram several years ago to explain to people why this delay exists and cannot be completely eliminated.

In a nutshell, if you target something and then try to have your followers immediately assist, they will pick up your old target. /assist is client-side, and your other clients will not have the information about your new target in order to correctly assist the new one, until the server has received the message that you targeted something new, and processes it in order to send out messages with your updated Target, and then your other clients receive and process the message. The amount of time this is, is basically directly related to your ping to the game server, probably about the same.

Here's the diagram.

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MiRai also showed this in a video: http://youtu.be/gkH06UNWFY0?t=1m46s

Source for all of this info: http://isboxer.com/wiki/Assist_delay