A tank of oxygen can explode but only if the tank of oxygen is ignited by a source of flame.
Without any flame or ignition source the tank of oxygen cannot catch fire or explode.
The way someone would catch fire when on an oxygen tank when smoking is that the heat from the cigarette is an ignition source.
That then catches the persons clothes etc on fire because the oxygen is fueling the fire from the cigarette.
All fires need oxygen to burn and the oxygen in the tank is a good fuel source to get the fire going so the oxygen can help the fire spread.
So that's why it's important to never smoke when you're using an oxygen tank to breathe with.
If you must smoke while on oxygen you should only do so when you're not using the oxygen tank and oxygen.
Because if the oxygen tank does get enough flame to it then yes it can eventually explode.
But just having a tank of oxygen in your car or house will not allow it to explode or catch fire unless you have an ignition source for it.