CEC can be used to turn devices on and off as well as set inputs. It often goes by other names but it's an industry standard. (Knowing the make and model of TV and AVR would clarify that.) In simple terms, you can turn devices on/off with CEC or by using the power button. Using both will produce unpredictable results. The new Telus remote could be the the issue. Another possibility is that a change in CEC compatibility between the Shaw and Telus boxes is causing the issue.
In an ideal world, turning on a source, such as the Telus box would cause CEC to turn the other required devices on and set all the correct inputs. There would be no need to press any other buttons. Some device remotes are programmed to automatically send power codes to the other devices in the system. The Telus remote (or other universal remote being used) may be programmed that way. That will cause unpredictable results if CEC is also enabled. If so, the answer may be to turn off the automatic power commands to other devices on the Telus remote. The method for doing this should be in the remote manual. Also make sure that the remote device codes for AVR, TV, etc are correct.
Use either CEC or power commands from the remote but not both. If the recommendation above does not work, some further investigation is necessary. I would disable automatic the sending of on/off codes to other components when a device is turned on. (This is done by programming the remotes.) Then, disable CEC on all devices. Check to see how the system works. It should be necessary to manually power devices on and off plus set the correct inputs. No devices should "magically" turn on or off or change input without direct control by it's own remote or the programed button on the master remote.
The next step would be to enable CEC on the TV and A/V receiver. Then turn on CEC for each device individually and test to see if this works correctly. Note which devices work correctly. If everything works properly you are all set. If not, a workaround or other fix might be needed. Activity based remotes (such as Harmony) are a good fix for systems where CEC or a standard universal remote do not work well.