It is assumed that the property has been titled in the name of the trust with you as trustee of the trust. Generally, as long as you are domestic partners at the time of death the real property taxes will not be reassessed upon his death. As with any law, there are some exceptions. You and your partner will want to discuss your facts and goals with an estate planning attorney or the attorney who set up your trust to ensure that trust does not contain any provisions which would circumvent the reassessment exclusion.
You need to talk with a tax attorney regarding this.
My offices does represent people from Avvo if they contact me but only in the Los Angeles, Orange, Ventura, San Bernardino and Riverside County in Southern California. The answers I give here are not meant to create an attorney client relationship. When accepting clients I conduct interviews face to face and they often take 30 minutes or more. I approach trials and issues from a legal and common sense approach, This is how the majority of judges I have appeared before in 40 years also make decisions. I do not intend by my advice to enter an attorney client relationship and in most cases advise to obtain legal representation. Sometimes if you can not afford it a consultation or limited scope representation is available. As an experienced attorney I can tell you, judges can be impatient, hate emotional arguments and over exagerations or lies. A brief outline of the problems and desired solutions is often best and I d0 limited scope representations advise clients on how to proceed at time of hearing or trial and my fees are considerably less when I do not appear in court as it takes much less of my time.
Just one quick clarification for anyone reading your question and the answers. You must be REGISTERED domestic partners for the transfer to be excluded from the definition of a "change in ownership", or from reassessment. You indicated that you have "filed", so you should be ok. But as always, you should have an attorney review your entire situation to ensure there will be property tax, or other, issues. Good luck.