Certain example embodiments of this invention relate to apparatuses for sealing the tips of pump-out tubes of vacuum insulating glass (VIG) units, and/or associated methods. In certain example embodiments, a laser source used in sealing the pump-out tube is thermally insulated from the VIG unit and emits a laser beam through one or more windows in an oven towards a mirror located therein. The mirror is located so as to redirect the laser beam onto the pump-out tube to thereby seal it. For instance, a substantially horizontal laser beam emitted from a laser source located outside the oven enters into the oven through one or more windows and is reflected by a mirror towards the pump-out tube to be sealed. The repositioning of the laser source advantageously can change its effective focal length and/or the location of the laser beam, e.g., because of the fixed location of the mirror.