100 Million times $10/month = $1 Billion per month. 3 months at $1 Billion/month = $3 Billion.
If this is going to be embedded in iOS 9, it seems very likely Apple will become King of the streaming space within hours after launch. This is just the Microsoft IE browser (vs. established Netscape) thing again.
And, since there is a 90-day free trial, Apple should be able to tout gigantic numbers of users pretty quickly. The key question will be monetizing free trials to stick around and start paying. The referenced rumor of 800 million iTunes accounts means about 1/8th of all iTunes users will need to not only partake in the free trial but convert to paying subscribers AND/OR that this will significantly draw more people into the iTunes total number of accounts pool..
As you have aluded to in your second paragraph, the measure of success would be in counting paid subscribers, especially after 1 year in and once more countries are on board, not in the hours and days after launch.
One other interesting bit of (obvious) math: $1 Billion/month times 12 months = $12 Billion new dollars for AAPL's revenue line.
You realise Apple doesn't get to keep the whole of that $10 pm itself right?