Lubavitcher Rebbe, Likutei Sichos 3 p945, https://www.chabad.org/therebbe/article_cdo/aid/93594/jewish/Shavuos.htm
With regard to the Counting of the Omer, however, the crossing of the dateline makes a significant difference. As mentioned above, the counting of the Omer is a mitzvah which is dependent on every person as an individual. Thus when a person crosses the dateline in the middle of counting the Omer, he must continue according to his own personal reckoning although everyone around him is counting a different day.
For example, Pesach falls on Shabbos. On Monday, the second day of the Counting of the Omer , a person travels from east to west [e.g., from the U.S. to Australia]. Although he left on Monday, when he crosses the dateline, it will be Tuesday. That night [the night between Tuesday and Wednesday], he is required to count the third day of the Omer, while the local people will be counting the fourth day.
Conversely, if a person crosses the dateline while traveling from west to east, leaving Monday and arriving on Monday, on the night between Monday and Tuesday, he must count the third day of the Omer, although the local people will be counting the second day.
(1) On the third new moon after the Israelites had gone forth from the land of Egypt, on that very day, they entered the wilderness of Sinai. (2) Having journeyed from Rephidim, they entered the wilderness of Sinai and encamped in the wilderness. Israel encamped there in front of the mountain, (3) and Moses went up to God. The LORD called to him from the mountain, saying, “Thus shall you say to the house of Jacob and declare to the children of Israel: (4) ‘You have seen what I did to the Egyptians, how I bore you on eagles’ wings and brought you to Me. (5) Now then, if you will obey Me faithfully and keep My covenant, you shall be My treasured possession among all the peoples. Indeed, all the earth is Mine, (6) but you shall be to Me a kingdom of priests and a holy nation.’ These are the words that you shall speak to the children of Israel.” (7) Moses came and summoned the elders of the people and put before them all that the LORD had commanded him. (8) All the people answered as one, saying, “All that the LORD has spoken we will do!” And Moses brought back the people’s words to the LORD. (9) And the LORD said to Moses, “I will come to you in a thick cloud, in order that the people may hear when I speak with you and so trust you ever after.” Then Moses reported the people’s words to the LORD, (10) and the LORD said to Moses, “Go to the people and warn them to stay pure today and tomorrow. Let them wash their clothes. (11) Let them be ready for the third day; for on the third day the LORD will come down, in the sight of all the people, on Mount Sinai. (12) You shall set bounds for the people round about, saying, ‘Beware of going up the mountain or touching the border of it. Whoever touches the mountain shall be put to death: (13) no hand shall touch him, but he shall be either stoned or shot; beast or man, he shall not live.’ When the ram’s horn sounds a long blast, they may go up on the mountain.” (14) Moses came down from the mountain to the people and warned the people to stay pure, and they washed their clothes. (15) And he said to the people, “Be ready for the third day: do not go near a woman.” (16) On the third day, as morning dawned, there was thunder, and lightning, and a dense cloud upon the mountain, and a very loud blast of the horn; and all the people who were in the camp trembled. (17) Moses led the people out of the camp toward God, and they took their places at the foot of the mountain. (18) Now Mount Sinai was all in smoke, for the LORD had come down upon it in fire; the smoke rose like the smoke of a kiln, and the whole mountain trembled violently. (19) The blare of the horn grew louder and louder. As Moses spoke, God answered him in thunder. (20) The LORD came down upon Mount Sinai, on the top of the mountain, and the LORD called Moses to the top of the mountain and Moses went up. (21) The LORD said to Moses, “Go down, warn the people not to break through to the LORD to gaze, lest many of them perish. (22) The priests also, who come near the LORD, must stay pure, lest the LORD break out against them.” (23) But Moses said to the LORD, “The people cannot come up to Mount Sinai, for You warned us saying, ‘Set bounds about the mountain and sanctify it.’” (24) So the LORD said to him, “Go down, and come back together with Aaron; but let not the priests or the people break through to come up to the LORD, lest He break out against them.” (25) And Moses went down to the people and spoke to them.