I used to work for a taxi-company and rear-ended another car. Taxi insurance company hired a lawyer. Can I trust him?

I am sorry, but your question is not clear. I am not sure what the "new matter" is or how it applies to what you are trying to describe. It is also not clear what you have been asked to sign.

The attorney hired by the insurance carrier for the Taxi Company has an ethical obligation to represent you.
The insurance on the cab protects you, up to the level of the limits of the liability insurance policy.
In Pennsylvania, an attorney for a defendant adds "New Matter" to an Answer to a Complaint, as a means of asserting affirmative defenses. The client has to sign a Verification to the Answer and New Matter, in which you are stating that the FACTS contained therein are true and correct.

I assume that the defense attorney is probably accurate that you are not an employee of the taxi company and that you lease the cab from the taxi company. If you have questions about the wording of the document, call the attorney and ask him to explain what his words mean. Go make an appointment and talk to the attorney. He has an obligation to communicate with you.

You will not have to pay for a part of the claim, UNLESS the plaintiff's injuries are so serious that the value of the claim is more than the amount of the insurance on the cab. Ask the attorney how much insurance coverage is available and how big the claim appears to be.

The short answer to your question is that the attorney hired by the insurance company must represent your interests as well as the taxi company's interests. If at some point those interests conflict, he will have a conflict and can ask the taxi company to hire an independent attorney. But at all times you should feel comfortable in asking questions of that attorney. He is your attorney.
Dale Larrimore