It appears to have been used before 2010.
I can't find sources for the "once a month" claim but there seems to be no lack of incidents involving US border forces firing tear gas into mexico.
This article, Dec 14, 2007
Mexico Says Border Patrol Assaulting Tijuana With Tear Gas
Mexican authorities and human rights groups said U.S. Border Patrol agents have begun launching pepper spray and tear gas from San Diego into densely populated Tijuana neighborhoods in response to escalating clashes with smugglers, it was reported Friday.
Border Patrol agents told the Los Angeles Times they have had to counter human traffickers' increasingly aggressive tactics -- especially near Tijuana's most notorious smuggling neighborhood of Colonia Libertad -- by ramping up their own use of force.
Agents have used pepper spray in the past, but usually aimed directly at the smugglers, according to the Times. The new tactics, which saturate large areas, have forced dozens of temporary evacuations and sent some residents to hospitals, witnesses told the newspaper.
Now the agency is responding with tear gas and powerful, pepper-spray weapons, including firing into Mexico.
The counteroffensive has drawn complaints that innocent families are being caught in the crossfire.
"A neighbor shouted, 'Stop it! There are children living here," said Esther Arias Medina, 41, who on Wednesday fled her Tijuana, Mexico, shanty with her 3-week-old grandson after the infant began coughing from smoke that seeped through the walls.
Jul 14, 2013
Texas DPS fires shots, launches tear gas across border
The Border Patrol agents then motioned toward Mexico, and Texas Rangers fired tear gas in that direction;