i9 Sports is speaking out after a controversial incident involving a 3-year-old at a soccer game sparked backlash ... and the youth sports organization says local league owners and team members are now receiving threats.

i9 Sports tells TMZ it reviewed what happened during Saturday's game in Winter Park, Florida, including interviews with people who were there and information available from police.

The league made it clear the call to police was NOT related to the child ... instead, a league official was reporting a disturbance between adults and seeking help de-escalating the situation.

i9 Sports says the official described the parents as "disruptive," but the organization doesn't have video of the actual confrontation and won't characterize the family beyond what was reported to police.

As we reported ... the Winter Park Police Department says no one was arrested, trespassed or forced to leave the park, and the matter was civil rather than criminal.

The league also confirms the family requested a refund, which was processed immediately, with confirmation sent October 24. Following the incident, i9 Sports says it asked the adults involved not to continue participating in the program.

i9 Sports says the response to the incident "has been intense" and they're now getting threats, which they say is not acceptable.

The org is pleading for the threats to stop and is asking folks not to share the names or photos of those involved, stressing that the focus should remain on supporting kids through sports.