Her 24-year-old partner, who wanted to be known only by his first name Itamar, said his family did not approve of their relationship.
They threatened to publicly shame him in Israel for "being gay" and wanted to commit him into a psychiatric hospital, he said.
"Itamar had to literally escape from his family and country with just the shirt on his back, just so we can be together," Miss Rubashkyn said.
She talked her mother into paying for Itamar's ticket to Auckland after his finances were frozen by his family.
Born Luis Alexander Rubashkyn, Miss Rubashkyn was referred for resettlement to New Zealand by the United Nations High Commissioner for Refugees.
She decided to migrate only after she was assured that her gender of preference could be issued in her travel documents without the need for sex-change surgery.
Miss Rubashkyn, who now has a New Zealand driver's licence and a job in flight operations support, said she met Itamar about eight months ago on a dating website.
"At first I did not share with him about my gender issues because I was afraid of how he will see me," she said.
"But when I finally did, I was overjoyed that he accepted me and continued to love me for who I am."
Itamar said he was "deep in love" with Miss Rubashkyn, and that it "did not matter" that she had not undergone sex-change surgery.
"In my eyes, she is a beautiful woman ... she is even more beautiful in person than on the computer screen," he said.
"I feel sad that I had to leave everything behind, including my family, but I have no regrets because now I am with my true love."
Itamar was detained by Immigration New Zealand officials at Auckland Airport because they did not think he was a bona fide visitor. He arrived in Auckland with no luggage, no credit card and very little money.
Itamar said he was questioned for two hours. He was released only after an immigration lawyer engaged by Miss Rubashkyn intervened.
He will apply for residency under the partnership category to remain in New Zealand after the wedding.
Immigration border manager Senta Jehle said Itamar arrived on May 19 and was eventually issued with a three-month visitor visa. "The call to Ms Rubashkyn was made as part of the verification process."
Ms Jehle said that to meet requirements, visitors must show a valid passport, a return ticket and sufficient funds to support their stay in New Zealand.