Clarification about Kaspersky Subscription

[WingRaith]

Around 3 weeks ago, I purchased another 2-year Kaspersky Premium subscription and activated it via the websites "Add activation code" feature and not via the desktop application.

However, in the last couple days I started receiving the pop-up messages warning me about my subscription ending, which seeing as I already purchased a subscription back then, I hypothetically shouldn't be receiving them.

So my question is, when the current subscription runs out, will the new 2 year subscription then activate and resume where the previous one left off, or will I have to re-download Kaspersky again in order to activate it because I activated it wrongly?