An attempt to explain: Some substances "find" some places on the stationary phase to which they bind strongly. Once these sites are covered with this substance the effect of essentially partially removing this substance from the chromatographic process will cease.
Now, I wonder what you mean with first time? The first time after washing or standing without flow......?
I can´t say that I have seen this thing with all analytes that were tried here. Even proteins, which have a tendency to do this, can be "tought" to behave if the proper mobile phase, stat phase is used. Of course, this is a matter of what you want to tolerate, if a certain amount of tailing is tolerated (or must be tolerated) one can also expect (and maybe tolerate) some lowering in early injections.