To stop Islam's expansion, you need to have them defeated when they attempt to go into Egypt, Persia, or Central Asia. If there is no conquest, Islam does not expand.
Of course, there will be some Muslims in other areas. As mentioned, Muslim traders will go out into the Indian Ocean. But Islam will have only limited success without the ability to impose political control over those areas. A minority of people, probably other traders in more urban areas, will be Muslim, but most will retain their indigenous religions.
Of course, in order to defeat each invasion, you will need multiple PODs. Much of the growth of early Islam was due to its ability to turn the inter-tribal raiding of the Arabs against others. Once united, the Arabs simply fought others instead of themselves. Victory in battle meant more loot, which attracted more men for the next invasion. Thus, it was a self-reinforcing project as future conquest meant more loot which attracted more men for the next invasion. It took a while for this force to be spent. So if the Muslim armies are defeated once, there will likely be subsequent invasions. Only when enough defeats are accumulated to discredit jihad as a source of greater wealth and glory will young men stop joining them. At that point, internal dissension will begin again and expansion stop. But given initial success and the wealth of its conquests in Syria and Iraq, this will take some time.
Essentially, the Byzantines need to hold onto Egypt, and the Persians need to rally. Both need to stop not one, but likely multiple invasions. It's theoretically possible, but would require a much different history with lots of good luck. There is no simply "change this" to make it work.
One possibility is for the Muslim armies to suffer some initial defeats when attacking Byzantium and Persia. A few early defeats may not mean the end of the attacks, but it would slow their momentum. If the Byzantimes won the Battle of Yarmuk, maybe they win the next battle too. Instead of easy conquests, the Muslims have a very difficult time. Perhaps the Muslim armies still manage to conquer Syria and Iraq, but only at substantial cost. By this time, the current Caliph dies, and a new one comes to power. Since the conquests are not easy, the new Caliph encourages a peace policy and comes to terms with Byzantium and Persia.