Interest on credit card balance

Lilibee

*EDIT* Just been doing some further reading and appears I am reading that correctly. Off to make the final payment of £33, cancel the DD and clear the account completely to save the extra half a month in interest.
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Hoping somebody can help explain this to me because I'm a little confused.

I had an existing balance of ~£2500 on a Virgin credit card. The last statement was recieved 8th June. On 13th June, I made a large payment leaving an outstanding balance of just £33.

I contacted Virgin to ask them to reduce the direct debit payment due to be applied on the 27th June because the amount they'd quoted on the statement was higher than the remaining balance of £33, so wanted to make sure the account didn't go into credit.

They replied to confirm this had been done, but also tacked the following sentences on to the message:

Please note that interest accrues daily on the outstanding balance until the full payment is received. The interest that accrued on the balance of £2418.44 from last statement date of 08 June until the full payment is received will be applied when the next statement is produced.

This reads like, for the purposes of applying residual interest on my next statement, they're going to assume that I had a balance of £2500 for the entire month, even though I actually only had this balance for the first 5 days.

Am I reading that correctly?