But their stark difference in tone during separate Friday meetings underlined a divide that has some asking: "Who speaks for America?"
Trump was in Virginia, meeting border protection officers and calling for harsher measures to deal with those "pouring in from El Salvador, Guatemala, Honduras, Mexico, all over."
Tillerson was on the Mexican leg of a Latin American tour, talking to local officials about a shared effort to combat international organized crime on both sides of the border.
At the Border Patrol National Targeting Center, Trump also heard about US efforts to partner with Latin American countries to stem the flow of drugs and illegal migrants.
But his response was scathing: "And what are Mexico and Colombia and these other countries - what are they doing about it? Nothing? Do you think they're really trying?"
Trump claimed that the United States was spending billions of dollars in aid to partner countries "and they're pouring drugs into our country and they're laughing at us."
And he explicitly linked the threat of drug gangs in America to migration from south of the border, underlining that this is the reason he is seeking to reform immigration law.
The night before Trump's latest outburst, Tillerson had dined in Mexico City with his Mexican counterpart Luis Videgaray and senior Mexican military and intelligence leaders.
And, as Trump was speaking, he was following up with three-way talks with Mexico and Canada on cross-border trade and law enforcement and hearing concerns about immigration rules.
He too stressed the importance of fighting the "transnational criminal organizations" Washington says are behind the opioid drug epidemic and violent crime on both sides of the border.
But he was careful to acknowledge that the United States has its own share of responsibility in having provided a market for drugs and allowing guns to be smuggled south to the cartels.
And, unlike Trump, he praised Mexico's efforts.
"So this is a joint effort that is very, very active, it is very robust, and we intend to maintain this effort well until we have resolved this problem," he told reporters.
So, is it a robust joint effort, or are the United States' Latin American friends not really trying?
This was not the first time Tillerson's diplomatic efforts abroad have been undercut by Trump's declarations at home.
Last year when Tillerson was in China and talking about holding open diplomatic channels to North Korea, Trump tweeted that he was "wasting his time."
Tillerson has also distanced himself publicly from the president a least once, saying that Trump was speaking "for himself" when he defended far-right demonstrators.
But, since reports last year - denied by the administration - that Tillerson had privately called Trump a "moron," officials have stressed they are on the same page.
Onboard Tillerson's plane from Mexico to his next set of delicate meetings in Argentina, one US official told reporters the president's remarks were "not helpful."
The secretary's closest aides would not criticize Trump directly, but stressed that Tillerson's more optimistic message reflects official US foreign policy.
Undersecretary of State for Public Diplomacy and Public Affairs Steve Goldstein said of Trump's remarks: "Different people speak different ways but the policy hasn't changed.
"And the secretary spoke about US foreign policy today," he added, noting that Tillerson felt he had made progress on deepening cooperation with Mexican authorities.
"We leave here feeling that we accomplished a great deal. We have more to do, but we're all on the same page and heading towards the same goal," Goldstein said.
Reform of America's immigration laws, including DACA, an initiative to shield more than a million undocumented people brought to America as children, is not Tillerson's job.
But, representing America in Mexico, he felt the need to acknowledge the "value of those people" and admit that it is "painful" for migrants to be living in uncertainty.
Or, as Goldstein described it later: "The secretary today in his meetings was stating US foreign policy as it relates to these issues, and he has respect for all people."
In Washington, foreign diplomats often complain of mixed signals from the administration, between the White House, the US mission at the United Nations and the State Department.
Columnists have started to suggest the United States has two policies, Trump's "America First" versus Tillerson and Defense Secretary Jim Mattis' cultivation of alliances.
Foreign leaders, wary of the disruptive effect of Trump's impulsive tweets, are careful not to publicly take sides.
But, when Tillerson addressed a news conference with Videgaray and Canada's foreign minister Chrystia Freeland, his international colleagues' choice of language was notable.
"I want to highlight the role and leadership of Secretary Tillerson, who has been instrumental to achieving this, and to bring our countries closer," Videgaray said.