Cherry, you did the best you could. The woman had said her phone would be turned off, and she's upset that someone left her a message? If I've told someone that my phone will be turned off, unless I tell them not to leave messages for me, I'd be glad that they had tried to call.
I really like BarensMom's response, it's the best option. Also, ask the technician if she would mind if you gave this woman her dedicated phone number (assuming she has one) or transfer the calls so she can leave them a voicemail directly. It might help if they're contacting each other without having someone else run interference for them, so at least the woman knows that her voicemail or messages are getting straight to the person who's going to be fixing them.
I've also had to tell our clients that the times they want us to call them are simply not possible and we need another way to contact them. We have fairly standard office hours and they'll want a phone call at 8:00 PM, for example, and will get extremely mad when we resort to leaving messages for them. I've been instructed by management to explain politely that we operate within certain hours, and if they did not provide us with an alternate method of contact (work phone number, cell phone number, email address) then we would be leaving messages during the day and getting messages the next morning, but there was no way of calling outside of certain hours. Might this be something you could do? Explain to the woman that your technician was scheduled for a meeting after 4:30 and would not be able to return a call after 5:00, so she called earlier to let the woman know that she had received her complaint and was working on it as quickly as she was able.