You are able to reposition the links when the host project republish the coordinates to the linked projects...
You asked if its normal and I just meant to say that yes it is a normal behavior what you experienced considering that there are several factors which may cause it and there several variable which one needs to check when repositioning fail...One of which is those links/elements being pinned; survey points being clipped...etc
I'm really sorry I can't give a definit answer.... I don't know the nature of the linked files which you refered to! Are you working on the local and where are the links (I would assume on the central - ideal to be)? did you check the linked instance properties in the host file? were the coordinate (supposedly shared) publish correctly and the links got updated? I can't be really sure what is going on on your side
I could have missed out on something...maybe one of the guys on the forum can share with us some thoughts on the matter