so basically you tier the gear before plusing it so your not taking any stats away from an item when your transmute it.
You tier the weapon. Tiering gear usually costs huge amounts for little return (unless you're using glorious and above stats, which make a mana stone tier 5, since most gear are at tier 4, so using these T5 mana stones will increase your equipment's tier by 1 at the same time for free).
The arcane transmuter also changes the tier. If you had an equipment that you previously tiered to tier 6, and you merge that equipment with 3 Tier 5 mana stones, the equipment drops to tier 5.
Also, statting and tiering both uses arcane transmuter, so that and transmuting is one and the same in this case.
You also want to plus (with plussing jewel, ex. Sun Jewel Faith) first, before you tier, stat, etc. Plussing jewels fail more when the equipment is statted.
And I'm not sure what you mean by tiering gear before statting/transmute it. When people do have the resources to tier gear, they do it at the same time as statting it.
There's a more advance guide on clean tiering on the forums (If someone who knows where it is could link it if OP needs please).