Yes, it apparently affected them through the water supply.
We see someone in the bathtub be affected by the Swooping Evil venom. Their face goes blank in a way that implies the venom took effect. We also see people drinking water forget as well. There are also water collection tanks on top of the roofs. The wizards are seen fixing them along with the rest of New York.
HIGH ANGLE pushing down toward the crowd as they look up to the sky. As the rain falls and hits them, people move on, docile - their bad memories washed away. Each person goes about their daily business as though nothing unusual has happened.
Aurors move through the streets, performing Repairing Charms to rebuild the city. Buildings and cars are reconstructed and streets are returned to normal.
ANGLE ON LANGDON, standing in the rain, his expression softening, growing blank as the water runs over his face.
ANGLE ON POLICE looking at their guns, confused - why do they have them drawn? They slowly gather themselves, putting their weapons away.
Inside a small family home, a young mother looks on fondly at her family. As she takes a sip of water, her expression becomes blank.
Groups of Aurors continue to repair the streets, swiftly reassembling broken tram tracks, all traces of destruction finally disappearing. One Auror, passing a newsstand, enchants the papers, removing NEWT and TINA’S mug shots and replacing them with banal headlines about the weather.
MR. BINGLEY, the bank manager, stands in his bathroom taking a shower. As the water trickles over him, he too is Obliviated. We see BINGLEY’S wife, brushing her teeth, her expression vacant, carefree.
FRANK continues to soar through the streets of New York, churning up more and more rain as he goes, his feathers shimmering a
brilliant gold. Finally he glides into the breaking New York dawn, a magnificent sight.
- Fantastic Beasts and Where to Find Them (The Original Screenplay)
But yes, the venom got into the water supply somehow. So presumably it would later affect people who were under an umbrella when they come into contact with the water in their water supply. Even under an umbrella, if they get splashed with the rain in some way, they'll be Obliviated before they even get inside. In addition, there are so many ways that people can come into contact with the water that avoiding it would be incredibly difficult. To avoid being Obliviated even if they stay indoors, they would have to not brush their teeth, take a shower, do the dishes, drink some water, or do anything else involving the use of water.
For the people who did not either get wet in the rain, or come into contact with water in any other way, which would be a small fraction of the population of New York, there are some possibilities that I can think of. The first is, it's never mentioned exactly how long the Swooping Evil venom stays active for. It could remain active for long enough where it would be impossible for people to avoid interacting with water in some way for that length of time.
The other thing is, the Aurors could still Obliviate whatever small part of the population had managed to somehow avoid any contact with water for however long it takes the venom to become ineffective. In addition, if there are any people who remember anything, it would be such a small amount that they could easily be written off as crazy. If someone starts rambling about the existence of wizards or creatures rampaging through the streets, since other people won't remember it, anyone who says anything about it will be thought of as insane.