You are correct. You have not personally licensed data from our company. Data was licensed to a company (our client), and you acted on their behalf and did their marketing campaign. So far so good, Then you decided to use the data for other campaigns for two of your other clients without properly licensing the data for those clients. Perhaps this was in error, perhaps it was deliberate. However, we were able to prove your use of this data, indeed we also sent you the information which showed what you had done. We sent you an invoice to enable you retrospectively to license the data for your clients as you should have done originally. I'm sure you noticed, we did not apply any penalty or interest for your misuse of our data - purely the correct commercial rate for the uses that had already taken place. Our objective was merely to put your usage on a proper legal base, to avoid exposing anyone to potential ramifications.
If you would like data for future clients we would of course be delighted to talk to you (or them) about the targeting for their campaign.
It is of course essential that you only use the data for the agreed purpose & I'm sure your clients would also wish to be certain that you will keep data they provide to you separate from data from other clients. As a processor, data protection laws, including GDPR require you to do so. Naturally, poor data hygiene is an issue for all companies, but especially if you are handling the client lists of your customers!