Futures Calendar Spread Quote Convention

Hoping to get this question answered on SExch so I don’t have to ask someone on the Desk and betray my ignorance.

Trading a Calendar Spread in equity derivatives involves selling/buying the near/far quarterly expirations of the same futures contract. I’m an execution trader so we execute these trades not to initiate an expression on the relative richness or cheapness of the calendar spread, but rather to roll our client’s current futures exposure from one contract expiry to the next.

The traders on my desk generally instruct roll trades using what I’ll call "long Roll/short Roll" convention:

"I can long roll 223x ESM1ESU1 @ -10.05 (selling M1, buying U1)"

"I can short roll 223x ESM1ESU1 @ -11.11 (buying M1, selling U1)"

That instruction makes sense, it’s explicit and unambiguous. We long roll when our clients are long in the current month and we short roll when our clients are short in the current month. Where I am getting confused is that most of our futures brokers provide quotes and axes using what I’ll call "buy roll/short roll" convention":

"We are axed to buy the ES roll up to 10000x"

"We are axed to sell the ES roll up to 30000x @ screen mid"

When a broker says they are "buying a roll" or "selling a roll", which contract is being bought and which is being sold?