Your new Invisalign trays are supposed to do one thing—gradually correct the misalignment of your teeth, with each successive tray repositioning your teeth until the correct alignment has been achieved. It helps that they're not especially noticeable, nor are they uncomfortable. Sure, there can be some mild irritation when you wear them for the first time, or when you change your trays for the next in the series. But this won't be prominent and will be short-lived. It can be a bit frustrating when your trays cause irritation in a place you don't expect—such as your tongue.
Your Tongue's Posture
Your tongue has a natural posture when it's not preoccupied with speaking and helping you to eat (amongst its many functions). This posture is against the roof of your mouth (your upper palate), often with the tip of your tongue resting against the backs of your upper central incisors. This natural posture, along with the range of motions that a tongue experiences, can bring it into regular contact with your Invisalign trays.
Your Invisalign Trays
The trays themselves are designed for orthodontic use (and comfortable orthodontic use at that). They're durable though lightweight thermoplastic, which shouldn't be irritating your tongue. However, the trays have a concave configuration, which allows them to be slotted over your teeth. This means that the trays have edges, and it might be that your tongue is regularly brushing against these edges, resulting in irritation and even mild lacerations.
Not a Standard Side Effect
Don't think that tongue irritation is an accepted side effect of using Invisalign. You won't need to put up with the problem for the duration of your treatment. You should contact your orthodontist, although they may recommend that the situation be monitored for the time being. Your tongue may well develop a tolerance to the stimulation from your trays, meaning the issue will correct itself.
Modifying Your Trays
If your irritation doesn't subside, a thorough assessment of your Invisalign trays will be needed. The solution is unlikely to be complicated. While your trays need to curve around your upper and lower dental arches, it's generally possible to modify the initial dimensions of the trays—only a tiny redesign will be needed. You may need new trays in a slightly different configuration, reducing the prominence of any sharp edges and eliminating their ability to irritate your tongue. It's going to be a small inconvenience but is better than simply living with an irritated tongue for the duration of your treatment.
The first advice from your orthodontist might be to wait and see for a brief period, but if your Invisalign trays continue to bother your tongue, there are ways for your orthodontist to take the edge off—in a manner of speaking.