Well, there are two aspects to changing your ISP:
1) The data portion
2) The Telkom circuit (often referred to as the line)
You can move the data portion without "migrating" the circuit. In other words, Telkom continue to manage your DSL line, and your ISP provisions you with the data. Or you can move both - the choice is yours.
The data portion is subjected to whatever terms your ISP and you agreed in your terms and conditions. With us, our customers can cancel in their current month, before the 19th. If you move your Telkom circuit to your ISP, Telkom will begin billing the ISP the moment the transfer is finalised, which takes a few days on average. If you were on a post-paid model with Telkom, you may still owe a month to them for the last month, which sometimes appears to be double-billing but is not - it's simply what happens when you move from a post-paid to a pre-paid payment model. If however Telkom bill for the month as well as your ISP, you can contact Telkom, show them the billing info from your ISP who will confirm the date upon which the "migration" was successful, and Telkom will credit that final payment of the DSL portion on your next invoice. In other words, the balance is "squared".
With regards to the data portion, I've not come across Telkom doing anything untoward here at all. If anything, simple human or systems errors can result in occasional issues but they are quick to resolve them.
With regards to the circuit portion, I've also not come across any untoward behaviour at all, and again, they are more than happy to resolve any billing issues that arise from a "migration" of the circuit to your ISP. In short, there's not much to concern yourself with - just get the info in writing.
Note that you cannot migrate the voice line rental and/or costs to your ISP at all at this time.