I believe you will need a a sub for each PS if you want them to be gaming online at the same time.
Just had a quick search and come across this from another site.
Yes, everyone needs their own PSN account, if they want to play.
Yes, he can use sub account from your account on another console.
Generally he would need separate PS+ subscription, as well as his separate games, but there is a "trick", one might say, to allow your PS+ and games to be playable by him, but there are some tradeoffs.
You have to deactivate your account as primary on your PS4.
You add your account on his PS4, and set it as primary console. This will make your PS+ and games available to all accounts on the console, including your son's. There is major but though.
Your console is no longer primary! Which means, you can play all your games and use your account online (PS+), but ONLY when you are online. Other accounts on your PS4 cannot use your games and PS+ either. The moment you are offline, or PSN is down, you will lose access to all your digital games.
There should be no issues with playing eachother, other than what was described in 3.3
Also found this:
I'm pretty sure that to get 3 consoles online at the same time, you will require 2 PS+ Subscriptions at least.
Console 1, 2, 3
A with the PS+, (B, C without)
Account A which has the PS+ can be loaded onto any console and reap the rewards of PS+
But Account A can only be a Primary Account to One Console at any given time.
Other Accounts that are on the console can take advantage of PS + and it's content.
Works well with 2 Consoles as you set the one Account that has PS+ to Primary and you can add a second Account, which in turn can use all the benefits of the Primary Account. You then just add the Account that has the PS + to the other Console as PS+ follows that Account to any Console.
As you have 3 consoles now, (how jealous some people are now), will result in having to buy another PS+
Looks like 2 Subscriptions for 3 consoles, the price of being greedy LOLz
And looking at what the Primary Account can share, you may have to buy 2 games/DLC to run 3 consoles as well. As only a Primary Account can share content.
For 2 Consoles, it works perfectly.
For 3.. [Console 1, 2, 3]
1. [Console 1] has the Primary Account (PS+) and is used by Player B with their own Account.
2. [Console 2] has the Primary Account that is created as a Non-Primary Account
3. [Console 3] has to buy Subscription and games/DLC