I'm going on the assumption you intend this to be a full cycle of 10 duals.
Positives: These seem balanced but not very strong (I'll get to that) and don't have any rules issues.
As a drawback its.. odd, primarily because lands without mana abilities really don't exist anymore aside of Fetch lands/Evolving wilds. Since Ice Age, only two lands have been printed w/o mana abilities that didn't sac to fetch something - Dark Depths and Eye of Ugin. The Latter still helped "pay for" things and the former was a throwback to Ice Age, so finding ways to effectively meet the untap condition are going to be difficult.
This makes their play pattern hard to maximize: Do I play a fetch land and then wait to crack it so I can get one of these untapped next turn?
I'm not sure why you're calling the "Reinforcement" lands either.
Adding "T: Add C" is going to be meaningless is almost every situation, so unless you are planning on putting this in a set like Oath of the Gatewatch it will just be clutter on the card.
I agree with Rowanalpha that this drawback is odd. I've no idea what the point of caring about this particular condition is supposed to be, flavour-wise or gameplay-wise. It just seems to be a thing you could design cards to care about without any real reason why you would do that. Just because a card design works and is balanceable does not make it fun or interesting.
I think it's also going to be a confusing condition for a lot of players. I reckon most players even will not know what this even works with on first look. I certainly didn't. My first thought was 'how many cards does that even apply to?'. Newer players I'm sure will struggle. I imagine some newer players will guess this is supposed to work with basic lands because they don't have any rules text. Taking one look at the google search results will reveal that plenty of people have been unsure about whether fetchlands count as mana abilities and I'm sure plenty of people as a result would miss that they work with this.
Mana abilities is a complex term to include on something as staple as dual lands and I think this condition is going to be more confusing than most usages of the term which are already relatively sparse.
alpha mox emerald
beta time walk
4 goyfs received
3 liliana of the veil
4 karn liberated
3 force of will
4 grove of the burnwillows
3 horizon canopy
2 full art damnation