"I do think absence makes the heart grow fonder," Savannah Guthrie tells PEOPLE (the TV Show!) while she and co-host Hoda Kotb detail their emotional reunions with their kids

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Hoda Kotb and Savannah Guthrie weren't expecting the welcome home they received from their kids upon returning from Japan.

The Today co-hosts recently got back from covering the Tokyo Olympics, documenting their emotional reunions with their families on their respective Instagrams. They told PEOPLE (the TV Show!) Thursday about coming home after two weeks overseas.

Kotb shares daughters Hope Catherine, 2, and Haley Joy, 4, with fiancé Joel Schiffman, and Guthrie and husband Michael Feldman have daughter Vale, 7 later this month, and son Charles "Charley" Max, 4½.

"I mean, I knew they loved me, but I was unaware of how much," says Kotb, 56. "When I walked in I was like, 'Oh my gosh,' because they just wouldn't let me go. It was beautiful. Finally I was like, 'Time for beddy-bye. Night, night. Mama's gotta go.' I started to feel dizzy like I was going to fall down!"

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Savannah Guthrie and Hoda Kotb
Credit: Nathan Congleton/NBC/NBCU Photo Bank via Getty Images

Guthrie, 49, adds, "We never are apart from our kids this long. Never. That's one of the joys of having this regular schedule. This is actually a great mom job — we're home every day, we get to spend our afternoons with our kids. So I do think absence makes the heart grow fonder."

Kotb added that her girls surprised her with welcome-back signs and the "sweetest" homemade presents for her.

Today's co-hosts recently told PEOPLE about how they'd been keeping in touch with their loved ones back home while stationed in Tokyo — plus the many souvenir requests they fielded. Kotb said her older child requested cookies, and Guthrie had the connection: "I have so many cookies [from a nearby convenience store]," she explained.

Guthrie, meanwhile, had secured "a lot of glittery" things for Vale, but told PEOPLE and her co-anchors that she needed a souvenir still for Charley and Feldman.

As for how her kids were cheering athletes on from home, Guthrie said, "Our kids are so excited. My kids are wearing their U.S.A. shirts, they're cheering on the teams. They're really thrilled that we're here — they can't believe I'm at the Olympics."

"We're making the time change work. I always tell them, 'I'm sending my sun to you' and 'Catch the moon. It's coming your way,' " she added at the time of coordinating calls with the time zone differences.