Every time my phone is out of Bluetooth range, my Vivosport alert me, and every time my phone is in range, my vivosport alert me.
How can I disable this alert?
Simply turn off Bluetooth on your phone or on the watch until you want to sync again. On the phone it is usualy quicker, since it is accessible over the top status bar. On some watches you can define a hot key combination, and assign it to the BT turning on/off, which may be even more convenient.