Unfortunately I think it is difficult, if not impossible, to explain all the territorial changes in map-form. We simply don't know enough about this period to draw definite boundaries. To take one example, that little green blob in Sicily during Caliph Uthman's tenure is literally only attested to in a single line in a single source:

Now that he [Olympius, a Roman general] had made peace with God’s holy church he mustered the army and set out for Sicily against the Saracen people who were living there.

We have no further information about this and it is generally assumed that this is evidence for an Arab raid in 652, but we don't know when the Arabs got there or even where they were on the island. One historian has even suggested that the scribe got it wrong and that originally it was referring to the Zarakianoi, a group of Moorish auxillaries settled on the island. Another example would be Egypt, which was first attacked in 640 and there was bitter fighting until 641, but then a truce was made and the Romans agreed to a treaty that handed Egypt to the Arabs a year afterwards - hence Egypt became a dominion of the Arabs in 642. The maps of course did not show this.

The same applies for other periods/regions too, since it does appear that there whilst there were a lot of raids/attacks into North Africa, Anatolia and the Transcaucasus, the imposition of a new government took a while to happen and normally only tribute was taken before the raiders went back to the Caliphate proper; this might explain why the map-maker made the size of the Caliphate under Uthman so big. As for the size of the empire under Ali, it is worth noting that the first Arab civil war occurred in 656, which was just yet another disaster for the Caliphate after their defeat at Constantinople in 654 and a major defeat in Armenia in 655, so the Romans made gains on all fronts against the weakened Arabs.

Unfortunately, the Arab conquests are very, very complicated and even academic historians can't provide a full definitive narrative yet, so I don't think I can describe everything that happened here. I can however recommend Robert Hoyland's In God's Path: The Arab Conquests and the Creation of an Islamic Empire (2014), which is a very up-to-date and readable narrative of this period. I'm afraid that the study of the seventh century has been transformed in the last few decades and a lot of the new findings have yet to filter down into sources like Wikipedia, hence why my account here may contradict some of what you know already. Hoyland's book is therefore I think the best way for you to get into this topic, which I can assure you is a fascinating one!