If you cancel your subscription, you will lose access immediately. You will not have access to content until the end of the month. This is not in my control and that is just how Patreon works.
If you downgrade your pledge, for example from $15 to $10, you will have access to the higher tier until the end of the month. On the next month, you will be billed the lower amount and you will then be at that lower tier.
If you decide to upgrade your pledge, like from $10 to 15, you will be billed the difference (this case $5, taxes might apply) and you will have access to the new tier immediately.