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A trial period is voluntary, and must be agreed to by the employer and employee in writing in good faith as part of an employment agreement. Did you sign this part of the contract?

The good faith provisions of the Employment Relations Act 2000 still apply to the negotiation of trial periods. Remedies are available for personal grievances other than those based on unjustified dismissal. For example, if employers act in a discriminatory manner or in the case of sexual or racial harassment, employees will be able to take a personal grievance under the Employment Relations Act through the Employment Relations Authority

Here it is arguable that they have not followed proper procedure of giving notice. They must still give you notice of 1 or 2 weeks.

So you can make a claim even though it is not as strong as if you were outside the 90 day period

If you have not signed a 90 day trial period, and there is no contract, then your employer has wrongly dismissed you, and will be fined for not having a contract. You can claim a full personal grievance and should get in to see a lawyer to start this.

By not having a contract he has broken the law. By not having a written agreement for the 90 days, then you are not on a trial period.