Writing on Twitter in Arabic, Jordanian Foreign Minister Ayman Safadi said the Syrians were allowed into the country following written commitments that Germany, Britain and Canada would resettle them following the operation.
"Syrian rockets were identified as having been launched as part of the internal fighting in Syria", said the Israeli army.
A Canadian government source told AFP that a second group of White Helmets and their relatives was also supposed to be evacuated but "could not reach the border because of the situation on the ground".
The search and rescue team has long claimed neutrality, but Syria, Russia and Iran dismiss the group as a propaganda arm of the rebels.
Damascus on Monday condemned the evacuation as a "criminal operation" undertaken by "Israel and its tools". Israel said it had helped with the evacuation at the request of US President Donald Trump and other leaders - and there had been fears that the workers' lives were at risk. "The lives of these people, who have saved lives, were now in danger". "Meanwhile, it is known perfectly well that the White Helmets have been involved in the most odious provocations during the conflict in Syria".
A Jordanian government source said 422 people were brought from Syria, over the Israeli-occupied Golan Heights frontier, and into Jordan, down from a figure of 800 announced earlier by the Foreign Ministry in Amman.
Israel seized 1,200 square kilometres (460 square miles) of the Golan from Syria in 1967, in a move never recognised internationally. They are authorized to remain in Jordan for a maximum of three months.
All other parties to the deal - Russia, Britain, France, Germany and China - have sought to keep it in effect, saying it is working as intended by preventing Iran from obtaining nuclear weapons for now. "The [White Helmets] are the bravest of the fearless and in a desperate situation this is at least one ray of hope", tweeted Jeremy Hunt, the British foreign secretary.
The source added "It has become unacceptable anymore to hold any meeting or discussions at the Organization for the Prohibition of Chemical Weapons (OPCW) or at any worldwide organizations to discuss their false allegations on the use of chemical weapon in Syria because there are not chemical weapons in Syria which hopes that the concerned global organizations will combat terrorism and that the OPCW will correct its stances and image which have been deeply affected after disclosing the true destructive role played by the "White Helmets" and others". Syrian officials have called the White Helmets a "terrorist group". No injuries or damage was reported, and the military says the rockets landed in Syrian territory.
Rescue operation evacuates over 100 White Helmets from Syria as Assad forces advance
But a volunteer in Daraa city, who asked to remain anonymous, said he had made a decision to stay despite being given the choice to leave.
Russia, the United States and Jordan made an arrangement in July 2017 to set up a de-escalation zone in southwestern Syria, embracing three southern governorates of the country - Deraa, Quneitra and As-Suwayda.
"We are first and foremost a humanitarian organisation, not a military one, or a terrorist one as the regime alleges".
Canada has been among several countries that have provided moral and financial support to the White Helmets, which are officially known as Syria Civil Defence, including $7.5 million over the past two years to help recruit and train women.
Since its formation, when Syria's conflict was nearing its third year, more than 250 of its volunteers have been killed. In 2017, a Netflix documentary about the group, "The White Helmets", won the Oscar for best documentary short.
Some members have received training overseas, including in Turkey, returning to instruct colleagues on search-and-rescue techniques.
The group receives funding from a number of Western governments and individual donors.
Regime forces have since regained control of most of these two provinces through a combination of deadly bombardment and Moscow-brokered surrender deals.
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