It seems like ta'veren, not the Power.
Here's the first passage you referred to:
"I'm ... lucky sometimes, Rand. let my luck choose. Head, the one that points to your right; flame, the other. What do you say?" [...] The coin spun into the air off Mat's thumb, gleaming dully in the sun. At its peak, Mat snatched it back and slapped it down on the back of his other hand, then hesitated. "It's a bloody thing to be trusting to the toss of a coin, Rand."
Rand laid his palm on one of the symbols without looking. "This one," he said. "You chose this one."
Mat peeked at the coin and blinked. "You're right. How did you know?"
"It has to work for me sooner or later." None of them understood - he could see that - but it did not matter.
If Rand was channelling, how would he even be able to affect the outcome? He doesn't see the result of Mat's toss (presumably he's too far away), and he doesn't know which symbol is the right one - he doesn't even look at which one he's indicating himself. While you can do many things with channelling, I don't think "giving yourself knowledge you didn't have before" is one of them. He could in theory have channelled Air to knock the coin the right way, but it would have needed a delicate weave, and at this point in the series he hasn't even had the tutelage to master channelling properly yet.
So I don't think Rand channelling could have accounted for what happened. It seems more likely to be the ta'veren effect, and Rand (perhaps somewhat arrogantly) assuming that it will work for him as he needs it to. Perhaps he's even relying on some sort of ta'veren link, a synchronicity between the effect for him and Mat, which means his blind choice and Mat's coin toss should give the same result.
And the second passage:
"We'll leave it to luck," [Mat] said, pulling the Tar Valon mark from his pocket. "Getting to be my lucky coin. Flame, I go in with you; head, I stay out." He flipped the gold coin quickly, before Rand could object.
Somehow he missed grabbing it; the mark careened off his fingertips, clinked to the pavement, bounced twice ... And landed on edge.
He glared at Rand accusingly. "Do you do this sort of thing on purpose? Can't you control it?"
"No." The coin fell over, showing an ageless woman's face surrounded by stars. "It looks like you stay out here, Mat."
"Did you just ... ?" He wished Rand would not channel around him. "Oh, burn me, if you want me to stay out here, I'll stay."
Here Mat thinks Rand is channelling - presumably this is what he's referring to by "do this sort of thing" - but again, the coin landing on edge seems more like a ta'veren effect. In some later book, Juilin (?) mentions that "Once, when Rand al'Thor was in Tear, I saw a tossed coin land on edge five times running ... in the end, we walked away and left it there." Freaks of chance with coin tosses are exactly the kind of thing the ta'veren effect can cause, inadvertently and all around.
The only thing that might have involved channelling was the coin falling over the "right" way - the way Rand wanted - after standing on edge for a moment. But again, this would have required very delicate flows of Air, and I don't think Rand can control the Power well enough at this stage to do such a thing. His lack of precision is exactly why the whole Asmodean thing happened (I'm being vague to avoid spoilers in case you haven't finished tSR yet).