Not sure what you mean. PaO2 refers only to the partial pressure of dissolved oxygen in arterial blood, there's no such thing as a PaO2 in interstitial tissue. If you are talking about interstitial PO2 that's a different thing though for purposes of the step the interstitial PO2 immediately adjacent to a capillary should be very close to capillary PaO2 in value. Also, as the capillary network is the most peripheral level of circulation, it is usually considered to be the same thing as "tissue level", so I'm unsure of how (or why?) you are making a distinction between the two.
As for your question, O2 unloading from the Hb happens in RBCs, to get into the tissues, the O2 must pass through the RBC membrane, through the blood, through the capillary walls, and into the tissue. During that transit through the blood, it becomes dissolved and contributes to the PaO2.
Think about it as people leaving a large auditorium through a small front lobby to go outside. (Outside=tissue, small lobby=PaO2, large auditorium=Hb, and people=O2) Initially, before the process started, the auditorium was full and the extra people that wouldn't fit had to stand in the lobby. Then when everyone is trying to leave, the people in the lobby leaves first and the people in the auditorium take their place. But since this is a continuous process, the lobby never becomes full again and instead, a continuous flow is established whereby the rate of people entering the lobby from the auditorium equals the rate of people leaving the lobby to go outside. During this period, the auditorium empties at the fastest rate and the number of people in the small lobby at any instant is constant and will remain so as long as there is enough people still left in the auditorium to sustain the flowrate of exiting people. Note, You can also say that anyone who has exited the building and is now outside must have passed through the small lobby. However, there is a distinction in that everyone outside must have passed through the lobby and so they were all in the lobby at some point in time, however only a small number of people were only in the lobby the entire time.