Exactly how you did.
Calling out a trainer in front of clients can be a big no-no, it breaks down the atmosphere of the gym. Keeping them as “professionals” is especially important and the image they represent can be injured when others see a social breakdown in the workplace.
Talking to them in private was a good call on your part- but maybe ask the trainer what they were working on. A big part of being a trainer is maintaining open communication with clients. Granted they should focus on who they are currently with but allow them some leniency to network.
I do it every now and then because I may need to reschedule with someone, but I keep the texting strictly professional. All of my personal texts wait till after work.
I agree that the way you handled it was probably the best at the moment. It allowed the training session to continue uninterrupted, it did not create a ‘scene’ by challenging the trainer in front of his client, and it allowed you to let the trainer know later that this was unacceptable. About the only thing that I would add would have been perhaps speaking with (apologizing to) the client later so that the client also understands and recognizes that you did notice this behavior and that you do not consider it acceptable (that their training hour is and should be devoted entirely to their training with no interruptions).
Yes pulling the trainer to the side after the session is done to address the issue is the best thing to do. Other than that being on your cell phone or listening to your iPod while your training a client is a BIG NO NO. Your clients pay good money to have your attention. That one hour that a client paid for they should have your full attention.
I have my phone with me at all times because many of my clients text to let me know if they are running late or whatever the matter may be. If I text in front of my client they know why and I tell them, it’s not a secret
With that being said, it’s best to have all electronic devices put away and yes the focus needs to be on our clients only!
Unless it’s an emergency, it can wait! It looks very unprofessional and the clients take notes because they are watching you all the time. If it’s someone who works for you, then it’s your reputation on the line as well. I would definitely confront my trainer and let him/her know that this can not happen again.