In the United States, I first heard the phrasal verb "to top up" used in fueling a car. To top up a car is to fill the tank to the very top, to put in as much more gas as it will hold. It is usually used when the tank is fairly full to begin with, so that you are not adding very much: "There's a gas station just ahead, do we need gas?" "The tank is 3/4 full, we don't really need gas, but to be safe I'll top it up anyway." By extension, it can be applied to other things. Since "to top up" a gas tank means "to fill it full," it makes the most sense if there is some natural maximum, or some standard amount. For example, you might decide that you want to start out each month with $500 on your card, so each month you would "top it up" to $500. It isn't normally used as a noun.

'Top up' is commonly used in British English. Like on a pay-as-you-go phone, you top it up when you buy more credit. Yes, it means exactly what you say, to add money or credit to something.

Yes, this can be expressed as a top-up. It can be used as a phrasal verb. I topped up, you top up, he tops up, etc...

Hello Robin. I've never heard the phrase "top-up". I'm wondering if maybe you're confusing it with "fill-up", but even in this context I would necessarily use that phrase. You might say refilled, "I refilled my membership card". Hope this helps.