Calamondin tree leaves turning yellow/brown

I would repot the healthy tree soon, after week or two, before new growth emerges, supposing, that spring is not far away in your location. But letting the tree still familiarize with changed environment and decrease its stress level after relocation from the store. And until repotting I wouldn't water it, unless the soil gets really too dry (I don't know your conditions, but usually it is better to keep your citruses on a dry side, than soggy). When repotting, I recommend to mix moist soil in advance, before putting the plant into the soil, and after planting maybe only add small amount of water (not flood it abundantly after planting, like it is common for repotting many other species). And it is useful to weigh the container with optimally moist soil, together with plant, so you know afterwards, how much water you must add when watering.
I am using my local soil, not commercial mixes, so I can't recommend you some trade mark or product. I have very sandy soil here, I just mix some compost and manure in the local soil, sometimes a little bit slow mineral fertilizers too. I decide about fertilizing and watering by look of leaves, how healthy they are. When the soil becomes too dry, leaves start to curl slightly or turn their angle from their usual position. The color of leaves hints when there is need for some fertilizers. You should select well draining mix, still enough organics in it. Avoid mixes, where organics like peat or coco choir are dominating. And you should prefer liquid fertilizers (if your plant has fruits on, it needs some special treatment with fertilizers). But better use more diluted solution, than too strong.

For your sick tree, I would not caused additional stress right now. Let the tree starts some growth first. As soon, as it starts to grow new leaves, treat it lightly with some diluted liquid fertilizer when watering. Repot after new growth is already strong enough. If this happens only when the weather is already unfavourable (there is a heat wave), then postpone repotting until late fall.

 

I have a section on transplanting (including repotting) in my growing citrus pages: Transplanting | Aprici

 

Because of some contradictions in suggestions by me and by Will B, I share some reasoning behind my suggestions.
1. Timing
Dormancy period until spring is generally the best time to repot trees. The worst time for repotting is when trees are just sprouted and have fresh shoots and leaves or when they bloom abuntantly or when plant has been under enormous stress (soil dried out for too long, some insect or disease damages, etc) recently. Of course, if there is rescue operation, like in case of root rot, then it is better to repot ASAP.
As mass production of young trees benefits from keeping containers rather small and light, it is usually beneficial for newly bought tree to up pot soon after bringing the tree to your home, as often the potting mix from the producer is as cheap and light as possible, and is already pretty much exhausted of nutrients for the end of shelf life in the shop. Specialized nurseries can afford strict regime of fertilizing and watering, so they can grow trees in a cheapest mix that is not so forgiving if overwatering happens or does not provide enough nutrients, as nutrients are dozed regularily by the tree nursery. Home plants usually have more irregular care and sometimes occasional neglect or mismanagement. There it is more important, that the soil provided enough nutrients, moisture and aeration even in case of some neglect or overwatering.
Your plant has crown large enough to be planted into larger container. Too large container isn't good either, as then the aeration in the soil may turn worse for longer periods after waterings. Containers larger than the volume of the crown, tend to be loo large for citruses.

2. Soaking the soil after repotting
Citruses don't like soggy soil, their roots benefit from good soil aeration. The risk of root rot is especially high, if the overwatering takes place during inactive season (dormancy) and when the container is large compared to the tree.
If you mix water into the potting soil before you plant, then it is easier to control optimal moisture level. The soil must be all wet, but not dripping wet. As root growth usually benefits from good soil aeration, and in the containers so small, it is easy to avoid detrimental large air pockets during repotting, it is wise to not soak the soil after planting, especially if it takes place before active growth. Trees replanted during active growth (lot of fresh shoots and leaves) or during heat vawe or being underwatered before repotting, may need some soaking after planting.