If you want to keep it really simple, you can detect word boundaries by checking two characters at a time. Here's a working example.
using namespace std;
#include <iostream>
#include <string>
#include <cctype>
typedef enum boundary_type_e {
    E_BOUNDARY_TYPE_ERROR = -1,
    E_BOUNDARY_TYPE_NONE,
    E_BOUNDARY_TYPE_LEFT,
    E_BOUNDARY_TYPE_RIGHT,
} boundary_type_t;
typedef struct boundary_s {
    boundary_type_t type;
    int pos;
} boundary_t;
bool is_word_char(int c) {
    return ' ' <= c && c <= '~' && !isspace(c) && c != ',';
}
boundary_t maybe_word_boundary(string str, int pos) {
    int len = str.length();
    if (pos < 0 || pos >= len) {
        return (boundary_t){.type = E_BOUNDARY_TYPE_ERROR};
    } else {
        if (pos == 0 && is_word_char(str[pos])) {
            // if the first character is word-y, we have a left boundary at the beginning
            return (boundary_t){.type = E_BOUNDARY_TYPE_LEFT, .pos = pos};
        } else if (pos == len - 1 && is_word_char(str[pos])) {
            // if the last character is word-y, we have a right boundary left of the null terminator
            return (boundary_t){.type = E_BOUNDARY_TYPE_RIGHT, .pos = pos + 1};
        } else if (!is_word_char(str[pos]) && is_word_char(str[pos + 1])) {
            // if we have a delimiter followed by a word char, we have a left boundary left of the word char
            return (boundary_t){.type = E_BOUNDARY_TYPE_LEFT, .pos = pos + 1};
        } else if (is_word_char(str[pos]) && !is_word_char(str[pos + 1])) {
            // if we have a word char followed by a delimiter, we have a right boundary right of the word char
            return (boundary_t){.type = E_BOUNDARY_TYPE_RIGHT, .pos = pos + 1};
        }
        return (boundary_t){.type = E_BOUNDARY_TYPE_NONE};
    }
}
int main() {
    string str;
    string ins_left("<tag>");
    string ins_right("</tag>");
    getline(cin, str);
    // can't use length for the loop condition without recalculating it all the time
    for (int i = 0; str[i] != '\0'; i++) {
        boundary_t boundary = maybe_word_boundary(str, i);
        if (boundary.type == E_BOUNDARY_TYPE_LEFT) {
            str.insert(boundary.pos, ins_left);
            i += ins_left.length();
        } else if (boundary.type == E_BOUNDARY_TYPE_RIGHT) {
            str.insert(boundary.pos, ins_right);
            i += ins_right.length();
        }
    }
}
It would be better to use enum class but I forgot the notation. You can also copy to a buffer instead of generating the new string in-place, I was just trying to keep it simple. Feel free to expand it to a class based C++ style. To get your exact desired output, strip the spaces first and add spaces to ins_left and ins_right.